global regularity for a class of 2d generalized tropical climate models abstract this paper establishes the global existence and regularity of solutions to a two dimensional 2d tropical climate model tcm with fractional dissipation the inviscid counterpart of this model was derived by frierson majda and pauluis 8 as a model for tropical geophysical flows this model reflects the interaction and coupling among the barotropic mode u the first baroclinic mode v of the velocity and the temperature the systems with fractional dissipation studied here may arise in the modeling of geophysical circumstances mathematically these systems allow simultaneous examination of a family of systems with various levels of regularization the aim here is the global regularity with the least dissipation we prove two main results first the global regularity of the system with v and for 1 and 3 2 and second the global regularity of the system with v for 3 2 the proofs of these results are not trivial and the requirements on the fractional indices appear to be optimal the key tools employed here include the maximal regularity for general fractional heat operators the littlewood paley decomposition and besov space techniques lower bounds involving fractional laplacian and simultaneous estimates of several coupled quantities

local well posedness for the maxwell schrodinger equation time local well posedness for the maxwell schrodinger equation in the coulomb gauge is studied in sobolev spaces by the contraction mapping principle the lorentz gauge and the temporal gauge cases are also treated by the gauge transform

a boundedness criterion for generalized calderon zygmund operators in 1965 a p calderon showed the l2 boundedness of the so called first calderon commutator this is one of the first examples of a non convolution operator associated to a kernel which satisfies certain size and smoothness properties comparable to those of the kernel of the hilbert transform these properties together with the l2 boundedness imply the lp boundedness for all p s in 1 oo many operators in analysis such as certain classes of pseudo differential operators and the cauchy integral operator on a curve are associated with kernels having these properties for these operators one of the major questions is if they are bounded on l2 we are going to give necessary and sufficient conditions for such an operator to be bounded on l2 they are essentially that the images of the function 1 under the actions of the operator and its adjoint both lie in bmo in the case of the aforementioned first commutator this can be checked by an integration by parts in the first section we present some basic notions and state the theorem which is proved in sections 2 and 3 in section 4 we show how to recover some classical results in sections 5 and 6 we construct a functional calculus for small perturbations of a and in section 7 we show a connection between the theory of calderon zygmund operators and kato s conjecture it is a pleasure to express our thanks to r r coifman and y meyer for suggesting many elegant simplifications in our proofs and most of the applications we also wish to thank stephen semmes for several pertinent remarks

stability and instability of solitary waves of korteweg de vries type considered herein are the stability and instability properties of solitary wave solutions of a general class of equations that arise as mathematical models for the unidirectional propagation of weakly nonlinear dispersive long waves special cases for which our analysis is decisive include equations of the korteweg de vries and benjamin ono type necessary and sufficient conditions are formulated in terms of the linearized dispersion relation and the nonlinearity for the solitary waves to be stable

the cauchy problem associated to the benjamin equation in weighted sobolev spaces abstract we study the initial value problem associated to the benjamin equation our purpose here is to establish persistence properties and some unique continuation properties of the solutions of this equation in weighted sobolev spaces

entropy pattern entropy and related methods for the analysis of data on the time intervals between heartbeats from 24 h electrocardiograms sequences of the time intervals between heartbeats char22 medically termed rr intervals char22 extracted from 24 h electrocardiogram recordings are examined as three dimensional return map images the recordings were made in humans by means of the medically widely used portable electrocardiograph holter system a time window measured in the number of heartbeats is used and different types of behavior are classified bifurcations between the types of dynamics of the heart are noted and a form of intermittency is found an alternative quantitative measure char22 a form pattern entropy of the return map image char22 is defined that characterizes the dynamics of the rr interval sequence it is shown that this is a measure of the degree of ordering of the rr interval sequence and as such it is a good novel medical diagnostic tool for analyzing heart rate variability which distinguishes between illness and health where other diagnostics fail

the sharp bound for the hilbert transform on weighted lebesgue spaces in terms of the classical ap characteristic we show that the norm of the hilbert transform as an operator in the weighted space l p r for 2 p oo is bounded by a constant multiple of the first power of the classical ap characteristic of this result is sharp we also prove a bilinear imbedding theorem with simple conditions

the ivp for a nonlocal perturbation of the benjamin ono equation in classical and weighted sobolev spaces abstract we prove that the initial value problem associated to a nonlocal perturbation of the benjamin ono equation is locally and globally well posed in sobolev spaces h s r for any s 3 2 and we establish that our result is sharp in the sense that the flow map of this equation fails to be c 2 in h s r for s 3 2 finally we study persistence properties of the solution flow in the weighted sobolev spaces z s r h s r l 2 x 2 r d x for s r 0 we also prove some unique continuation properties of the solution flow in these spaces

splitting methods for the nonlocal fowler equation we consider a nonlocal scalar conservation law proposed by andrew c fowler to describe the dynamics of dunes and we develop a numerical procedure based on splitting methods to approximate its solutions we begin by proving the convergence of the well known lie formula which is an approximation of the exact solution of order one in time we next use the split step fourier method to approximate the continuous problem using the fast fourier transform and the finite difference method our numerical experiments confirm the theoretical results

non uniform dependence on initial data for the two component novikov system considered herein is the initial value problem for the two component novikov system it is shown that the solution map of this problem is not uniformly continuous in sobolev spaces hs hs 1 for s 5 2 on the line based on the well posedness result and the lifespan for this problem the method of approximate solutions is utilized

on uniqueness properties of solutions of the k generalized kdv equations in this paper we study uniqueness properties of solutions of the so called k generalized korteweg de vries equations our goal is to obtain sufficient conditions on the behavior of the difference u1 u2 of two solutions u1 u2 of 1 1 at two different times t0 0 and t1 1 which guarantee that u1 u2

the well posedness of the korteweg de vries benjamin ono equation abstract the well posedness of the cauchy problem to the generalized korteweg de vries benjamin ono equation is considered local results for data in h s r s 1 8 and the global well posedness for data in l 2 r are obtained if l 2 moreover for l 3 the problem is locally well posed for data in hs s 1 4 the main idea is to use the fourier restriction norm method

global well posedness for the benjamin equation in low regularity abstract in this paper we consider the initial value problem of the benjamin equation t u h x 2 u x 3 u x u 2 0 where u r 0 t r and the constants r 0 we use the i method to show that it is globally well posed in sobolev spaces h s r for s 3 4 moreover we use some argument to obtain a good estimative for the lifetime of the local solution and employ some multiplier decomposition argument to construct the almost conserved quantities

how random is your heart beat we measure the content of random uncorrelated noise in heart rate variability using a general method of noise level estimation using a coarse grained entropy we show that usually except for atrial fibrillation the level of such noise is within 5 15 of the variance of the data and that the variability due to the linearly correlated processes is dominant in all cases analyzed but atrial fibrillation the nonlinear deterministic content of heart rate variability remains significant and may not be ignored

well posedness of stochastic kdv bo equation driven by fractional brownian motion the cauchy problem for the korteweg de vries benjamin ono equation driven by cylindrical fractional brownian motion is discussed in this paper fractional brownian motion is a family of processes b h it is known that the smaller the value of hurst parameter h is the worse of the regularity of fbm is using bourgain restriction method we obtain the lower bound of the hurst parameter h for the driving processes b h with h 38 we prove local existence results with initial value in classical sobolev spaces of negative indices i e h s with s 18

nonselfadjoint schrodinger operators with singular first order coefficients schrodinger operators of the form t i grad b x 2 a x grad q x in r m are considered where a b ate real vector valued functions and q is a scalar complex valued function it is shown that t is essentially quasi m accretive in l 2 r m if 1 x2223 1 a l 4 l div a l and re q 0 the proof is elementary

asymptotic expansion of solutions to the drift diffusion equation with fractional dissipation abstract the initial value problem for the drift diffusion equation arising from the model of semiconductor device simulations is studied the dissipation on this equation is given by the fractional laplacian 2 large time behavior of solutions to the drift diffusion equation with 0 1 is discussed when 1 large time behavior of solutions is known however when 0 1 the perturbation methods used in the preceding works would not work in this paper the asymptotic expansion of solutions with high order is derived

rasim a novel rotation and scale invariant matching of local image interest points this paper presents a novel algorithm for matching image interest points potential interest points are identified by searching for local peaks in difference of gaussian dog images we refine and assign rotation scale and location for each keypoint by using the sift algorithm pseudo log polar sampling grid is then applied to properly scaled image patches around each keypoint and a weighted adaptive lifting scheme transform is designed for each ring of the log polar grid the designed adaptive transform for a ring in the reference keypoint and the general non adaptive transform are applied to the corresponding ring in a test keypoint similarity measure is calculated by comparing the corresponding transform domain coefficients of the adaptive and non adaptive transforms we refer to the proposed versatile system of rotation and scale invariant matching as rasim our experiments show that the accuracy of rasim is more than sift which is the most widely used interest point matching algorithm in the literature rasim is also more robust to image deformations while its computation time is comparable to sift

a note on the ostrovsky equation in weighted sobolev spaces abstract in this work we consider the initial value problem ivp associated to the ostrovsky equations u t x 3 u x 1 u u x u 0 x r t r u x 0 u 0 x we study the well posedness of the ivp in the weighted sobolev spaces z s s 2 f h s r x 1 f l 2 r l 2 x s d x with 3 4 s 1

scale affine invariant interest point detectors in this paper we propose a novel approach for detecting interest points invariant to scale and affine transformations our scale and affine invariant detectors are based on the following recent results 1 interest points extracted with the harris detector can be adapted to affine transformations and give repeatable results geometrically stable 2 the characteristic scale of a local structure is indicated by a local extremum over scale of normalized derivatives the laplacian 3 the affine shape of a point neighborhood is estimated based on the second moment matrix our scale invariant detector computes a multi scale representation for the harris interest point detector and then selects points at which a local measure the laplacian is maximal over scales this provides a set of distinctive points which are invariant to scale rotation and translation as well as robust to illumination changes and limited changes of viewpoint the characteristic scale determines a scale invariant region for each point we extend the scale invariant detector to affine invariance by estimating the affine shape of a point neighborhood an iterative algorithm modifies location scale and neighborhood of each point and converges to affine invariant points this method can deal with significant affine transformations including large scale changes the characteristic scale and the affine shape of neighborhood determine an affine invariant region for each point we present a comparative evaluation of different detectors and show that our approach provides better results than existing methods the performance of our detector is also confirmed by excellent matching resultss the image is described by a set of scale affine invariant descriptors computed on the regions associated with our points

template matching based object recognition with unknown geometric parameters we examine the problem of locating an object in an image when size and rotation are unknown previous work has shown that with known geometric parameters an image restoration method can be useful by estimating a delta function at the object location when the geometric parameters are unknown this method becomes impractical because the likelihood surface to be minimized across size and rotation has numerous local minima and areas of zero gradient we propose a new approach where a smooth approximation of the template is used to minimize a well behaved likelihood surface a coarse to fine approximation of the original template using a diffusion like equation is used to create a library of templates using this library we can successively perform minimizations which are locally well behaved as detail is added to the template the likelihood surface gains local minima but previous estimates place us within a well behaved bowl around the global minimum leading to an accurate estimate numerical experiments are shown which verify the value of this approach for a wide range of values of the geometric parameters

global well posedness of the kp i initial value problem in the energy space we prove that the kp i initial value problem begin cases partial tu partial x 3u partial x 1 partial y 2u partial x u 2 2 0 text on mathbb r 2 x y times mathbb r t u 0 phi end cases is globally well posed in the energy space mathbf e 1 mathbb r 2 big phi mathbb r 2 to mathbb r phi mathbf e 1 mathbb r 2 approx phi l 2 partial x phi l 2 big partial x 1 partial y phi big l 2 infty big

the ivp for the benjamin ono zakharov kuznetsov equation in low regularity sobolev spaces abstract in this paper we study the initial value problem associated with the benjamin ono zakharov kuznetsov equation such equation appears as a two dimensional generalization of the benjamin ono equation when transverse effects are included via weak dispersion of zakharov kuznetsov type we prove that the initial value problem is locally well posed in the usual l 2 r 2 based sobolev spaces h s r 2 s 11 8 and in some weighted sobolev spaces to obtain our results most of the arguments are accomplished taking into account the ones for the benjamin ono equation

derf distinctive efficient robust features from the biological modeling of the p ganglion cells studies in neuroscience and biological vision have shown that the human retina has strong computational power and its information representation supports vision tasks on both ventral and dorsal pathways in this paper a new local image descriptor termed distinctive efficient robust features derf is derived by modeling the response and distribution properties of the parvocellular projecting ganglion cells in the primate retina derf features exponential scale distribution exponential grid structure and circularly symmetric function difference of gaussian dog used as a convolution kernel all of which are consistent with the characteristics of the ganglion cell array found in neurophysiology anatomy and biophysics in addition a new explanation for local descriptor design is presented from the perspective of wavelet tight frames dog is naturally a wavelet and the structure of the grid points array in our descriptor is closely related to the spatial sampling of wavelets the dog wavelet itself forms a frame and when we modulate the parameters of our descriptor to make the frame tighter the performance of the derf descriptor improves accordingly this is verified by designing a tight frame dog which leads to much better performance extensive experiments conducted in the image matching task on the multiview stereo correspondence data set demonstrate that derf outperforms state of the art methods for both hand crafted and learned descriptors while remaining robust and being much faster to compute

multiscale multifractal analysis of heart rate variability recordings with a large number of occurrences of arrhythmia human heart rate variability in the form of time series of intervals between heart beats shows complex fractal properties recently it was demonstrated many times that the fractal properties vary from point to point along the series leading to multifractality in this paper we concentrate not only on the fact that the human heart rate has multifractal properties but also that these properties depend on the time scale in which the multifractality is measured this time scale is related to the frequency band of the signal we find that human heart rate variability appears to be far more complex than hitherto reported in the studies using a fixed time scale we introduce a method called multiscale multifractal analysis mma which allows us to extend the description of heart rate variability to include the dependence on the magnitude of the variability and time scale or frequency band mma is relatively immune to additive noise and nonstationarity including the nonstationarity due to inclusions into the time series of events of a different dynamics e g arrhythmic events in sinus rhythm the mma method may provide new ways of measuring the nonlinearity of a signal and it may help to develop new methods of medical diagnostics

on the propagation of regularity and decay of solutions to the benjamin equation in this paper we investigate some special regularities and decay properties of solutions to the initial value problem of the benjamin equation the main result shows that for initial datum u0 hs r with s 3 4 if the restriction of u0 belongs to hl x0 for some l z and x0 r then the restriction of the corresponding solution u t belongs to hl for any r and any t 0 t consequently this type of regularity travels with infinite speed to its left as time evolves

global well posedness and inviscid limit for the korteweg de vries burgers equation abstract considering the cauchy problem for the korteweg de vries burgers equation u t u x x x x 2 u u 2 x 0 u 0 where 0 1 and u is a real valued function we show that it is globally well posed in h s s s and uniformly globally well posed in h s s 3 4 for all 0 1 moreover we prove that for any t 0 its solution converges in c 0 t h s to that of the kdv equation if tends to 0

existence of a local smooth solution in probability to the stochastic euler equations in r3 abstract we establish the existence of a local smooth solution of the stochastic euler equations in r 3 probabilistic estimate of the random time interval for the existence of a local solution is expressed in terms of expected values of the initial data and the random noise there are numerous works on the stochastic euler equations in a two dimensional domain even for the deterministic euler equations in a three dimensional domain the only results are concerned with the local existence of smooth solutions our goal is to extend such local existence result to the stochastic equations

nonlinear dynamics of the heartbeat i the av junction passive conduit or active oscillator under physiologic conditions the av junction is traditionally regarded as a passive conduit for the conduction of impulses from the atria to the ventricles an alternative view namely that subsidiary pacemakers play an active role in normal electrophysiologic dynamics during sinus rhythm has been suggested based on nonlinear models of cardiac oscillators a central problem has been the development of a simple but explicit mathematical model for coupled nonlinear oscillators relevant both to stable and perturbed cardiac dynamics we use equations describing an analog electrical circuit with an external d c voltage source v0 and two nonlinear oscillators with intrinsic frequencies in the ratio of 3 2 comparable to the sa node and av junction rates the oscillators are coupled by means of a resistor 1 1 sa av phase locking of the oscillators occurs over a critical range of v0 externally driving the sa oscillator at increasing rates results in 3 2 av wenckebach periodicity and a 2 1 av block these findings appear with no assumptions about conduction time or refractoriness this dynamical model is consistent with the new interpretation that normal sinus rhythm may represent 1 1 coupling of two or more active nonlinear oscillators and also accounts for the appearance of an av block with critical changes in a single parameter such as the pacing rate

gevrey regularity for a class of water wave models abstract local well posedness for a class of higher order nonlinear dispersive partial differential equations is obtained in spaces of functions analytic on a strip around the real axis the proof relies on estimates in space time norms adapted to the linear part of the equation the class of equations in view contains a number of equations arising in the modeling of waves in fluids and also in other applications

a novel rotation scale invariant template matching algorithm using weighted adaptive lifting scheme transform this paper presents a novel algorithm for detecting user selected objects in given test images based on a new adaptive lifting scheme transform given an object as a template we first select a set of coefficients as object features in the wavelet transform domain and then build an adaptive transform based on the selected features the goal of the new adaptive transform is to vanish the selected features in the transform domain after applying both non adaptive and adaptive transforms to a given test image the corresponding transform domain coefficients are compared for detecting the object of interest in addition the proposed detection algorithm is combined with the proper log polar mapping model in the parametric template space to attain rotation scale invariance property finally we have verified the properties of our proposed algorithm with experimental results

fractional derivative estimates in gevrey spaces global regularity and decay for solutions to semilinear equations in rn abstract we propose a unified functional analytic approach to study the uniform analytic gevrey regularity and the decay of solutions to semilinear elliptic equations on r n first we develop a fractional calculus for nonlinear maps in banach spaces of l p based gevrey functions 1 h p s r n regularity with s scr 0 depending on the nonlinearity next we investigate the type of decay polynomial or exponential of the derivatives of solutions to semilinear elliptic equations provided they decay a priori slowly as o x x for some small 0 the restrictions involved in our results are optimal in particular given a hyperplane l we construct 2d 2 strongly singular solutions locally in h p s r n for s

l2global well posedness of the initial value problem associated to the benjamin equation abstract we study well posedness for the initial value problem associated to the benjamin equation and the periodic benjamin equation global results are established for data inl2 r andl2 t respectively we apply the recent theory developed by kenig ponce and vega and bourgain to deal with low regularity data for the initial value problem associated to the korteweg de vries equation

a comparison of affine region detectors the paper gives a snapshot of the state of the art in affine covariant region detectors and compares their performance on a set of test images under varying imaging conditions six types of detectors are included detectors based on affine normalization around harris mikolajczyk and schmid 2002 schaffalitzky and zisserman 2002 and hessian points mikolajczyk and schmid 2002 a detector of maximally stable extremal regions proposed by matas et al 2002 an edge based region detector tuytelaars and van gool 1999 and a detector based on intensity extrema tuytelaars and van gool 2000 and a detector of salient regions proposed by kadir zisserman and brady 2004 the performance is measured against changes in viewpoint scale illumination defocus and image compression the objective of this paper is also to establish a reference test set of images and performance software so that future detectors can be evaluated in the same framework

weighted gradient estimates for the parabolic p laplacian equations abstract in this paper we obtain the weighted l q estimates of the gradients of weak solutions for the quasilinear parabolic equations of p laplacian type with small bmo coefficients for every e 0 q 1 if u p l w l o c 1 e t and f p l w l o c q t then we prove that u p l w l o c q t our results improve the known results for such equations using a harmonic analysis free technique

sharp well posedness and ill posedness results for a quadratic non linear schrodinger equation abstract we establish that the quadratic non linear schrodinger equation iu t u xx u 2 where u r r c is locally well posed in h s r when s 1 and ill posed when s 1 previous work in c kenig g ponce l vega quadratic forms for the 1 d semilinear schrodinger equation trans amer math soc 346 1996 3323 3353 had established local well posedness for s 3 4 the local well posedness is achieved by an iteration using a modification of the standard x s b spaces the ill posedness uses an abstract and general argument relying on the high to low frequency cascade present in the non linearity and a computation of the first non linear iterate

sharp well posedness for the benjamin equation abstract having the ill posedness in the range s 3 4 of the cauchy problem for the benjamin equation with an initial h s r data we prove that the already established local well posedness in the range s 3 4 of this initial value problem is extendable to s 3 4 and also that such a well posed property is globally valid for s 3 4

recurrence plot based measures of complexity and their application to heart rate variability data the knowledge of transitions between regular laminar or chaotic behaviors is essential to understand the underlying mechanisms behind complex systems while several linear approaches are often insufficient to describe such processes there are several nonlinear methods that however require rather long time observations to overcome these difficulties we propose measures of complexity based on vertical structures in recurrence plots and apply them to the logistic map as well as to heart rate variability data for the logistic map these measures enable us not only to detect transitions between chaotic and periodic states but also to identify laminar states i e chaos chaos transitions the traditional recurrence quantification analysis fails to detect the latter transitions applying our measures to the heart rate variability data we are able to detect and quantify the laminar phases before a life threatening cardiac arrhythmia occurs thereby facilitating a prediction of such an event our findings could be of importance for the therapy of malignant cardiac arrhythmias

well posedness of the muskat problem with h2 initial data abstract we study the dynamics of the interface between two incompressible fluids in a two dimensional porous medium whose flow is modeled by the muskat equations for the two phase muskat problem we establish global well posedness and decay to equilibrium for small h 2 perturbations of the rest state for the one phase muskat problem we prove local well posedness for h 2 initial data of arbitrary size finally we show that solutions to the muskat equations instantaneously become infinitely smooth

the zakharov kuznetsov equation in weighted sobolev spaces abstract in this work we consider the initial value problem ivp associated to the two dimensional zakharov kuznetsov equation u t x 3 u x y 2 u u x u 0 x y r 2 t r u x y 0 u 0 x y we study the well posedness of the ivp in the weighted sobolev spaces h s r 2 l 2 1 x 2 y 2 r d x d y with s r r

the ivp for the benjamin ono zakharov kuznetsov equation in weighted sobolev spaces abstract in this paper we study the initial value problem associated with the benjamin ono zakharov kuznetsov equation we prove that the ivp for such equation is locally well posed in the usual sobolev spaces h s r 2 s 2 and in the anisotropic spaces h s 1 s 2 r 2 s 2 2 s 1 s 2 we also study the persistence properties of the solution and local well posedness in the weighted sobolev class z s r h s r 2 l 2 1 x 2 y 2 r d x d y where s 2 r 0 and s 2 r unique continuation properties of the solution are also established these continuation principles show that our persistence properties are sharp

decay estimates for a class of wave equations abstract in this paper we use a unified way studying the decay estimate for a class of dispersive semigroup given by e i t where r r is smooth away from the origin especially the decay estimates for the solutions of the klein gordon equation and the beam equation are simplified and slightly improved

multilinear weighted convolution of l 2 functions and applications to nonlinear dispersive equations the x s b spaces as used by beals bourgain kenig ponce vega klainerman machedon and others are fundamental tools to study the low regularity behavior of nonlinear dispersive equations it is of particular interest to obtain bilinear or multilinear estimates involving these spaces by plancherel s theorem and duality these estimates reduce to estimating a weighted convolution integral in terms of the l 2 norms of the component functions in this paper we systematically study weighted convolution estimates on l 2 as a consequence we obtain sharp bilinear estimates for the kdv wave and schrodinger x s b spaces

stability theory of solitary waves in the presence of symmetry ii abstract consider an abstract hamiltonian system which is invariant under a group of operators we continue to study the effect of the group invariance on the stability of solitary waves applications are given to bound states and traveling wave solutions of nonlinear wave equations

homoclinic chaos in chemical systems abstract we first focus on complex dynamical phenomena generated by chemical kinetics in homogeneous media we comment on the alternating sequences of periodic and chaotic states observed in some experiments on the belousov zhabotinsky reaction when conducted in a continuously stirred tank reactor we present numerical results obtained with a seven variable oregonator model which reproduce most of the features of the experimental sequences we discuss the origin and the nature of the chemical chaos encountered along these sequences in terms of the chaotic orbits which exist on the way to homoclinicity we construct poincare map models which reduce to either multi humped or multi branched 1d maps in the strong area contraction limit we report on a recent experiment which provides evidence that the iteration scheme deduced from the time series of spiral type strange attractors satistifies the symbolic dynamics predicted by sil nikov theory of homoclinic chaos we then investigate spatio temporal pattern forming phenomena in a one dimensional reaction diffusion system with equal diffusion coefficients when imposing a concentration gradient through the system this model mimics the sustained stationary and periodically oscillating front structures observed in recent experiments conducted in an open couette flow reactor we emphasize the possibility that the oscillations of the spatial structure become chaotic we report on numerical simulations of a diffusion induced intermittent bursting phenomenon that is likely to be observed in bench experiments we elaborate on the interpretation of this intermittent occurrence of spatially localized structures in an extended system in terms of sil nikov s homoclinic chaos

remarks on a paper by j t beale t kato and a majda we prove that the maximum norm of the deformation tensor controls the possible breakdown of smooth solutions for the 3 dimensional euler equations more precisely the loss of regularity in a local smooth solution of the euler equations implies the growth without bound of the deformation tensor as the critical time approaches equivalently if the deformation tensor remains bounded the existence of a smooth solution is guaranteed

global weak solution and blow up criterion of the general ericksen leslie system for nematic liquid crystal flows abstract in this paper we investigate the three dimensional general ericksen leslie e l system with ginzburg landau type approximation modeling nematic liquid crystal flows first by overcoming the difficulties from lack of maximum principle for the director equation and high order nonlinearities for the stress tensor we prove existence of global in time weak solutions under physically meaningful boundary conditions and suitable assumptions on the leslie coefficients which ensures that the total energy of the e l system is dissipated moreover for the e l system with periodic boundary conditions we prove the local well posedness of classical solutions under the so called parodi s relation and establish a blow up criterion in terms of the temporal integral of both the maximum norm of the curl of the velocity field and the maximum norm of the gradient of the liquid crystal director field

solitary wave solutions of the benjamin equation considered here is a model equation put forward by benjamin that governs approximately the evolution of waves on the interface of a two fluid system in which surface tension effects cannot be ignored our principal focus is the traveling wave solutions called solitary waves and three aspects will be investigated a constructive proof of the existence of these waves together with a proof of their stability is developed continuation methods are used to generate a scheme capable of numerically approximating these solitary waves the computer generated approximations reveal detailed aspects of the structure of these waves they are symmetric about their crests but unlike the classical korteweg de vries solitary waves they feature a finite number of oscillations the derivation of the equation is also revisited to get an idea of whether or not these oscillatory waves might actually occur in a natural setting

sufficient conditions for stability of solitary wave solutions of model equations for long waves abstract we consider solitary wave solutions of model equations for long waves that feature a general form of linear dispersion sufficient conditions for the non linear stability of such solutions are derived these conditions are shown to obtain for the korteweg de vries equation and certain of its generalizations such as the benjamin ono equation and the intermediate long wave equation

analytical behavior of two dimensional incompressible flow in porous media in this paper we study the analytic structure of a two dimensional mass balance equation of an incompressible fluid in a porous medium given by darcy s law we obtain local existence and uniqueness by the particle trajectory method and we present different global existence criterions these analytical results with numerical simulations are used to indicate nonformation of singularities moreover blow up results are shown in a class of solutions with infinite energy

a numerical scheme for periodic travelling wave simulations in some nonlinear dispersive wave models a numerical method for simulating periodic travelling wave solutions of some nonlinear dispersive wave equations is proposed the construction of the scheme is based on an efficient computation of the elements that characterize these solutions the initial profile and the velocity of the wave

symmetry of minimizers for some nonlocal variational problems abstract we present a new approach to study the symmetry of minimizers for a large class of nonlocal variational problems this approach which generalizes the reflection method is based on the existence of some integral identities we study the identities that lead to symmetry results the functionals that can be considered and the function spaces that can be used then we use our method to prove the symmetry of minimizers for a class of variational problems involving the fractional powers of laplacian for the generalized choquard functional and for the standing waves of the davey stewartson equation

direct observation of homoclinic orbits in human heart rate variability homoclinic trajectories of the interbeat intervals between contractions of ventricles of the human heart are identified the interbeat intervals are extracted from 24 h holter ecg recordings three such recordings are discussed in detail mappings of the measured consecutive interbeat intervals are constructed in the second and in some cases in the fourth iterate of the map of interbeat intervals homoclinic trajectories associated with a hyperbolic saddle are found the homoclinic trajectories are often persistent for many interbeat intervals sometimes spanning many thousands of heartbeats several features typical for homoclinic trajectories found in other systems were identified including a signature of the gluing bifurcation the homoclinic trajectories are present both in recordings of heart rate variability obtained from patients with an increased number of arrhythmias and in cases in which the sinus rhythm is dominant the results presented are a strong indication of the importance of deterministic nonlinear instabilities in human heart rate variability

lyapunov stability of ground states of nonlinear dispersive evolution equations on presente une nouvelle demonstration de la stabilite orbitale des solitons d etat fondamental de l equation de schrodinger non lineaire pour une grande classe de non linearites on demontre la stabilite de l onde solitaire pour l equation de korteweg de vries generalisee

on the propagation of regularities in solutions of the benjamin ono equation abstract we shall deduce some special regularity properties of solutions to the ivp associated to the benjamin ono equation mainly for datum u 0 h 3 2 r whose restriction belongs to h m b for some m z m 2 and b r we shall prove that the restriction of the corresponding solution u t belongs to h m for any r and any t 0 therefore this type of regularity of the datum travels with infinite speed to its left as time evolves

existence and stability of solitary wave solutions of equations of benjamin bona mahony type abstract we consider solitary wave solutions of equations of benjamin bona mahony type we show that for a large class of equations of bbm type there do exist stable sets consisting of solitary wave profile functions in the case of generalized bbm equations we found that there are profile functions of stable solitary waves that are not the minimizers of the associated variational problem such a phenomenon is not known to exist for equations of korteweg de vries type

the ivp for the benjamin ono equation in weighted sobolev spaces abstract in this work we continue our study initiated in fonseca and ponce 2011 11 on the uniqueness properties of real solutions to the ivp associated to the benjamin ono bo equation in particular we shall show that the uniqueness results established in fonseca and ponce 2011 11 do not extend to any pair of non vanishing solutions of the bo equation also we shall prove that the uniqueness result established in fonseca and ponce 2011 11 under a hypothesis involving information of the solution at three different times cannot be relaxed to two different times

the hormander multiplier theorem for multilinear operators in this paper we provide a version of the mikhlin hormander multiplier theorem for multilinear operators in the case where the target space is l p for pe 1 this extends a recent result of tomita 15 who proved an analogous result for p 1

weighted gradient estimates for the general elliptic p x laplacian equations abstract in this paper we obtain the weighted l q estimates of the gradients of weak solutions for the general elliptic p x laplacian equations div a x u div f p x 2 f under some proper assumptions on a p f we prove that f p x l w loc q u p x l w loc q for any q 1

remarks on the breakdown of smooth solutions for the 3 d euler equations the authors prove that the maximum norm of the vorticity controls the breakdown of smooth solutions of the 3 d euler equations in other words if a solution of the euler equations is initially smooth and loses its regularity at some later time then the maximum vorticity necessarily grows without bound as the critical time approaches equivalently if the vorticity remains bounded a smooth solution persists

instability of nonlinear dispersive solitary waves we consider linear instability of solitary waves of several classes of dispersive long wave models they include generalizations of kdv bbm regularized boussinesq equations with general dispersive operators and nonlinear terms we obtain criteria for the existence of exponentially growing solutions to the linearized problem the novelty is that we dealt with models with nonlocal dispersive terms for which the spectra problem is out of reach by the evans function technique for the proof we reduce the linearized problem to study a family of nonlocal operators which are closely related to properties of solitary waves a continuation argument with a moving kernel formula is used to find the instability criteria these techniques have also been extended to study instability of periodic waves and of the full water wave problem

well posedness of the initial value problem for the korteweg de vries equation 1 1 itu axu u1xu o x t e r u x 0 uo x the kdv equation which was first derived as a model for unidirectional propagation of nonlinear dispersive long waves 21 has been considered in different contexts namely in its relation with the inverse scattering method in plasma physics and in algebraic geometry see 24 and references therein our purpose is to study local and global well posedness of the ivp 1 1 in classical sobolev spaces hs r we shall say that the ivp 1 1 is locally resp globally well posed in the function space x if it induces a dynamical system on x by generating a continuous local resp global flow it was established in the works of bona and smith 3 bona and scott 2 saut and temam 30 and kato 1 5 that the ivp 1 1 is locally resp globally well posed in hs with s 3 2 resp s 2 roughly speaking global well posedness in hs depends on the available local theory and on the conservation laws satisfied by solutions of 1 1 namely

pattern dynamics near inverse homoclinic bifurcation in fluids we report the pattern dynamics in the vicinity of an inverse homoclinic bifurcation in an extended dissipative system we observe in direct numerical simulations of three dimensional rayleigh benard convection with stress free top and bottom plates a spontaneous breaking of a competition of two mutually perpendicular sets of oscillating cross rolls to one of two possible sets of oscillating cross rolls as the rayleigh number is raised above a critical value the time period of the oscillating cross roll patterns diverges and shows scaling behavior near the bifurcation point this is an example of a transition from nonlocal to local pattern dynamics near an inverse homoclinic bifurcation we also present a simple four mode model that captures the pattern dynamics quite well

continuity properties of the solution map for the generalized reduced ostrovsky equation abstract it is shown that the data to solution map for the generalized reduced ostrovsky gro equation is not uniformly continuous on bounded sets in sobolev spaces on the circle with exponent s 3 2 considering that for this range of exponents the gro equation is well posed with continuous dependence on initial data this result makes the continuity of the solution map an optimal property however if a weaker h r topology is used then it is shown that the solution map becomes holder continuous in h s

sharp local well posedness results for the nonlinear wave equation this article is concerned with local well posedness of the cauchy problem for second order quasilinear hyperbolic equations with rough initial data the new results obtained here are sharp in low dimension

global weighted estimates in orlicz spaces for second order nondivergence parabolic equations abstract in this paper we prove the following global weighted estimates in orlicz spaces f l w t u d u d 2 u u t l w t for second order parabolic equations of nondivergence form with small bmo coefficients u t a i j x t u x i x j f in t u x t 0 on p t

a bilinear estimate with applications to the kdv equation u x 0 u0 x where u0 h r our principal aim here is to lower the best index s for which one has local well posedness in h r i e existence uniqueness persistence and continuous dependence on the data for a finite time interval whose size depends on u0 hs equation in 1 1 was derived by korteweg and de vries 21 as a model for long wave propagating in a channel a large amount of work has been devoted to the existence problem for the ivp 1 1 for instance see 9 10 the inverse scattering method applies to this problem and under appropriate decay assumptions on the data several existence results have been established see 5 6 14 28 33 another approach inherited from hyperbolic problems relies on the energy estimates and in particular shows that 1 1 is locally well posed in h r for s 3 2 see 2 3 12 29 30 31 using these results and conservation laws global in time well posedness in h r s 2 was established see 3 12 30 also global in time weak solutions in the energy space h r were constructed in 34 in 13 and 22 a local smoothing effect for solutions of 1 1 was discovered this combined with the conservation laws was used in 13 and 22 to construct global in time weak solutions with data in h r and even in l r in 16 we introduced oscillatory integral techniques to establish local well posedness of 1 1 in h r s 3 4 and hence global in time well posedness in h r s 1 in 16 we showed how to obtain the above mentioned result by picard iteration in an appropriate function space in 4 j bourgain introduced new function spaces adapted to the linear operator t 3 x for which there are good bilinear estimates for the nonlinear term x u 2 using these spaces bourgain was able to establish local well posedness of 1 1 in h r l r and hence by a conservation

on well posedness for the benjamin ono equation we prove existence and uniqueness of solutions for the benjamin ono equation with data in h s mathbb r s 1 4 moreover the flow is holder continuous in weaker topologies