on the structural stability of the euler voigt and navier stokes voigt models abstract we consider the euler voigt equations and the navier stokes voigt equations which are obtained by an inviscid regularization from the corresponding equations the main result we show is the structural stability of the system in terms of the variations of both viscosity and regularization parameters

global solutions to the two dimensional quasi geostrophic equation with critical or super critical dissipation the two dimensional quasi geostrophic 2d qg equation with critical and super critical dissipation is studied in sobolev space h s 2 for critical case open image in new window existence of global large solutions in h s is proved for s open image in new window when open image in new window is small this generalizes and improves the results of constantin d cordoba and wu 4 for s 1 2 and the result of a cordoba and d cordoba 8 for s open image in new window for s 1 these solutions are also unique the improvement for pushing s down from 1 to open image in new window is somewhat surprising and unexpected for super critical case 0 open image in new window existence and uniqueness of global large solution in h s is proved when the product open image in new window is small for suitable s 2 2 p 1 and 0 1

on the motion of non homogeneous fluids in the presence of diffusion in this paper we study the motion of a non viscous fluid consisting of two components both incompressible say saturated salt water and water taking into consideration the diffusion among these components the equations of the model are obtained for example in frank and kamenetskii 6 and the viscous case is studied in ignat ev and kuznetsov 8 and kazhikhov and smagulov 9 lo for a presentation of this kind of problems see also kuznetsov 111 observe that in s lo the problem is solved only for fluids whose viscosity d is sufficiently large i e

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

on the solutions in the large of the two dimensional flow of a nonviscous incompressible fluid abstract the euler equations 1 1 for the motion of a nonviscous imcompressible fluid in a plane domain are studied let e be the banach space defined in 1 4 let the initial data v 0 belong to e and let the external forces f t belong to l loc 1 r e in theorem 1 1 the strong continuity and the global boundedness of the unique solution v t are proved and in theorem 1 2 the strong continuous dependence of v on the data v 0 and f is proved in particular the vorticity rot v t is a continuous function in gw for every t r if and only if this property holds for one value of t in theorem 1 3 some properties for the associated group of nonlinear operators s t are stated finally in theorem 1 4 a quite general sufficient condition is given on the data in order to get classical solutions

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

nonlinear evolution equations and the euler flow abstract a new theorem on abstract nonlinear equations of evolution is proved as an application the existence uniqueness regularity and continuous dependence on the data are proved for the solution of the euler equation for incompressible fluids in a bounded domain in r m

the existence and uniqueness of the local solution for a camassa holm type equation a shallow water equation of camassa holm type containing nonlinear dissipative effect is investigated using the techniques of the pseudoparabolic regularization and some prior estimates derived from the equation itself we establish the existence and uniqueness of its local solution in sobolev space h s r with s 32 meanwhile a new lemma and a sufficient condition which guarantee the existence of solutions of the equation in lower order sobolev space h s with 1

stability of solitary waves and weak rotation limit for the ostrovsky equation abstract ostrovsky equation describes the propagation of long internal and surface waves in shallow water in the presence of rotation in this model dispersion is taken into account while dissipation is neglected existence and nonexistence of localized solitary waves is classified according to the sign of the dispersion parameter which can be either positive or negative it is proved that for the case of positive dispersion the set of solitary waves is stable with respect to perturbations the issue of passing to the limit as the rotation parameter tends to zero for solutions of the cauchy problem is investigated on a bounded time interval

downstream evolution of proper orthogonal decomposition eigenfunctions in a lobed mixer a two dimensional one space and time scalar adaptation of the proper orthogonal decomposition was applied to streamwise velocity data obtained in a lobed mixer flowfield using a rake of 15 single component hot wires through the application of the proper orthogonal decomposition the amount of streamwise turbulent kinetic energy contained in the various proper orthogonal modes was examined for two different downstream locations z h 2 6 and 3 9 the large eddy or dominant mode was shown to have a measurable decrease in the relative streamwise component of the kinetic energy between these two downstream locations this indicates that the large eddy as defined by the proper orthogonal decomposition breaks down and the flow becomes more homogeneous a pseudoflow visualization technique was then employed to help visualize this process

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

the existence of global strong and weak solutions for the novikov equation abstract the well posedness of the global strong and weak solutions for the novikov equation is investigated provided that initial value u 0 h s s 3 2 and satisfying a sign condition the existence and uniqueness of global strong solutions for the equation are shown to be valid in sobolev space the estimates in h q r space with 0 q 1 2 which are derived from the equation itself are developed to prove the existence and uniqueness of the global weak solutions

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

a well posedness theorem for non homogeneous inviscid fluids via a perturbation theorem on applique un theoreme de perturbation pour montrer le caractere bien pose d equations hyperboliques non lineaires application a une equation d ecoulement

a nonsymmetric state variable decomposition for modal analysis a modal decomposition strategy based on state variable ensembles is formulated a nonsymmetric generalized eigenvalue problem is constructed the data based eigenvalue problem is related to the generalized eigenvalue problem associated with free vibration solutions of the state variable formulation of linear multi degree of freedom systems for linear free response data the inverse transpose of the eigenvector matrix converges to the state variable modal eigenvectors and the eigenvalues of the nonsymmetric eigenvalue problem approximate those of the state variable model as such the eigenvalues lead to estimates of frequencies and modal damping the interpretation holds for linear systems with multi modal free responses whether damping is small or somewhat large modal or nonmodal and without the need of input data

fair multiuser channel allocation for ofdma networks using nash bargaining solutions and coalitions in this paper a fair scheme to allocate subcarrier rate and power for multiuser orthogonal frequency division multiple access systems is proposed the problem is to maximize the overall system rate under each user s maximal power and minimal rate constraints while considering the fairness among users the approach considers a new fairness criterion which is a generalized proportional fairness based on nash bargaining solutions and coalitions first a two user algorithm is developed to bargain subcarrier usage between two users then a multiuser bargaining algorithm is developed based on optimal coalition pairs among users the simulation results show that the proposed algorithms not only provide fair resource allocation among users but also have a comparable overall system rate with the scheme maximizing the total rate without considering fairness they also have much higher rates than that of the scheme with max min fairness moreover the proposed iterative fast implementation has the complexity for each iteration of only o k sup 2 nlog sub 2 n k sup 4 where n is the number of subcarriers and k is the number of users

a review on some contributions to perturbation theory singular limits and well posedness abstract in the beginning of the 1990s we devoted a sequence of papers to perturbation theory singular limits and well posedness problems in particular the strong well posedness of the initial boundary value problem for the compressible euler equations was demonstrate for the first time our method also allowed singular limit results in the strong norm even under assumptions weaker than the current ones in the literature where the strong norm is not reached it is worth noting that until now the above method and results have not been substantially improved hence an introduction to it still looks timely actually in a forthcoming paper by returning to this method we improve in a very substantial way some important results recently appeared in the literature

image denoising with dominant sets by a coalitional game approach dominant sets are a new graph partition method for pairwise data clustering proposed by pavan and pelillo we address the problem of dominant sets with a coalitional game model in which each data point is treated as a player and similar data points are encouraged to group together for cooperation we propose betrayal and hermit rules to describe the cooperative behaviors among the players after applying the betrayal and hermit rules an optimal and stable graph partition emerges and all the players in the partition will not change their groups for computational feasibility we design an approximate algorithm for finding a dominant set of mutually similar players and then apply the algorithm to an application such as image denoising in image denoising every pixel is treated as a player who seeks similar partners according to its patch appearance in its local neighborhood by averaging the noisy effects with the similar pixels in the dominant sets we improve nonlocal means image denoising to restore the intrinsic structure of the original images and achieve competitive denoising results with the state of the art methods in visual and quantitative qualities

well posedness travelling waves and geometrical aspects of generalizations of the camassa holm equation abstract in this paper we consider a five parameter equation including the camassa holm and the dullin gottwald holm equations among others we prove the existence and uniqueness of solutions of the cauchy problem using kato s approach conservation laws of the equation up to second order are also investigated from these conservation laws we establish some properties for the solutions of the equation and we also find a quadrature for it the quadrature obtained is of capital importance in a classification of bounded travelling wave solutions we also find some explicit solutions given in terms of elliptic integrals finally we classify the members of the equation describing pseudo spherical surfaces

two stage image denoising by principal component analysis with local pixel grouping this paper presents an efficient image denoising scheme by using principal component analysis pca with local pixel grouping lpg for a better preservation of image local structures a pixel and its nearest neighbors are modeled as a vector variable whose training samples are selected from the local window by using block matching based lpg such an lpg procedure guarantees that only the sample blocks with similar contents are used in the local statistics calculation for pca transform estimation so that the image local features can be well preserved after coefficient shrinkage in the pca domain to remove the noise the lpg pca denoising procedure is iterated one more time to further improve the denoising performance and the noise level is adaptively adjusted in the second stage experimental results on benchmark test images demonstrate that the lpg pca method achieves very competitive denoising performance especially in image fine structure preservation compared with state of the art denoising algorithms

optimal spatial adaptation for patch based image denoising a novel adaptive and patch based approach is proposed for image denoising and representation the method is based on a pointwise selection of small image patches of fixed size in the variable neighborhood of each pixel our contribution is to associate with each pixel the weighted sum of data points within an adaptive neighborhood in a manner that it balances the accuracy of approximation and the stochastic error at each spatial position this method is general and can be applied under the assumption that there exists repetitive patterns in a local neighborhood of a point by introducing spatial adaptivity we extend the work earlier described by buades et al which can be considered as an extension of bilateral filtering to image patches finally we propose a nearly parameter free algorithm for image denoising the method is applied to both artificially corrupted white gaussian noise and real images and the performance is very close to and in some cases even surpasses that of the already published denoising methods

the infinite number of generalized dimensions of fractals and strange attractors abstract we show that fractals in general and strange attractors in particular are characterized by an infinite number of generalized dimensions dq q 0 to this aim we develop a rescaling transformation group which yields analytic expressions for all the quantities dq we prove that lim q 0 dq fractal dimension d limq 1dq information dimension and dq 2 correlation exponent v dq with other integer q s correspond to exponents associated with ternary quaternary and higher correlation functions we prove that generally dq dq for any q q for homogeneous fractals dq dq a particularly interesting dimension is dq for two examples feigenbaum attractor generalized baker s transformation we calculate the generalized dimensions and find that d is a non trivial number all the other generalized dimensions are bounded between the fractal dimension and d

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

an improved regularity criterion for the 3d hall mhd equations via the vorticity abstract in this paper we consider the three dimensional incompressible hall magnetohydrodynamic equations and establish an improved regularity criterion of local in time classical solutions involving only the vorticity field consequently this improves the previous result

well posedness and blow up phenomena for a higher order shallow water equation this paper deals with the cauchy problem for a higher order shallow water equation yt auxy buyx 0 where y 2ku i x2 ku and k 2 the local well posedness of solutions for the cauchy problem in sobolev space hs r with s 7 2 is obtained under some assumptions the existence and uniqueness of the global solutions to the equation are shown and conditions that lead to the development of singularities in finite time for the solutions are also acquired finally the weak solution for the equation is considered

nonlocal image and movie denoising neighborhood filters are nonlocal image and movie filters which reduce the noise by averaging similar pixels the first object of the paper is to present a unified theory of these filters and reliable criteria to compare them to other filter classes a ccd noise model will be presented justifying the involvement of neighborhood filters a classification of neighborhood filters will be proposed including classical image and movie denoising methods and discussing further a recently introduced neighborhood filter nl means in order to compare denoising methods three principles will be discussed the first principle method noise specifies that only noise must be removed from an image a second principle will be introduced noise to noise according to which a denoising method must transform a white noise into a white noise contrarily to method noise this principle which characterizes artifact free methods eliminates any subjectivity and can be checked by mathematical arguments and fourier analysis noise to noise will be proven to rule out most denoising methods with the exception of neighborhood filters this is why a third and new comparison principle the statistical optimality is needed and will be introduced to compare the performance of all neighborhood filters the three principles will be applied to compare ten different image and movie denoising methods it will be first shown that only wavelet thresholding methods and nl means give an acceptable method noise second that neighborhood filters are the only ones to satisfy the noise to noise principle third that among them nl means is closest to statistical optimality a particular attention will be paid to the application of the statistical optimality criterion for movie denoising methods it will be pointed out that current movie denoising methods are motion compensated neighborhood filters this amounts to say that they are neighborhood filters and that the ideal neighborhood of a pixel is its trajectory unfortunately the aperture problem makes it impossible to estimate ground true trajectories it will be demonstrated that computing trajectories and restricting the neighborhood to them is harmful for denoising purposes and that space time nl means preserves more movie details

well posedness and blow up solutions for an integrable nonlinearly dispersive model wave equation abstract we establish local well posedness in the sobolev space hs with any s 3 2 for an integrable nonlinearly dispersive wave equation arising as a model for shallow water waves known as the camassa holm equation however unlike the more familiar korteweg devries model we demonstrate conditions on the initial data that lead to finite time blow up of certain solutions

on the dual systems to euler and navier stokes equations in r3 in this paper we consider two model systems of equations obtained by taking the hodge duals of the euler and the navier stokes systems respectively the vorticity formulation of the new system becomes a nonlinear non local scalar equation having similarities to the quasi geostrophic equations we prove the local existence of classical solutions and derive the beale kato majda type of blow up criterion for the dual euler system moreover we actually show that the finite time blow up occurs for generic non trivial initial data for this system for the dual navier stokes equations we construct an explicitly global in time smooth solution for general initial data using the hopf cole transform in the appendix we formulate the euler system and the dual euler system in terms of the clifford algebra

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 cauchy problem for a generalized camassa holm equation abstract in this paper we are concerned with the cauchy problem of the generalized camassa holm equation using a galerkin type approximation scheme it is shown that this equation is well posed in sobolev spaces h s s 3 2 for both the periodic and the nonperiodic case in the sense of hadamard that is the data to solution map is continuous furthermore it is proved that this dependence is sharp by showing that the solution map is not uniformly continuous the nonuniform dependence is proved using the method of approximate solutions and well posedness estimates moreover it is shown that the solution map for the generalized camassa holm equation is holder continuous in h r topology finally with analytic initial data we show that its solutions are analytic in both variables globally in space and locally in time

on the vanishing viscosity limit of 3d navier stokes equations under slip boundary conditions in general domains we consider the vanishing viscosity limit for the navier stokes equations with certain slip without friction boundary conditions in a bounded domain with non flat boundary in particular we are able to show convergence in strong norms for a solution starting with initial data belonging to the special subclass of data with vanishing vorticity on the boundary the proof is obtained by smoothing the initial data and by a perturbation argument with quite precise estimates for the equations of the vorticity and for that of the curl of the vorticity

a complex orthogonal decomposition for wave motion analysis a method is presented for decomposing wave motion into its principle components the basic idea is a complex generalization of proper orthogonal decomposition the method involves the representation of real oscillatory signals as complex analytic signals the relationship between complex modes and wave motion is explored from an ensemble of complex signals a complex correlation matrix is formed and its complex eigensolution is the basis of the decomposition like a complex singular value decomposition the complex eigenvectors contain standing and traveling characteristics a traveling index is proposed to quantify the relative degree of traveling and standing in a waveform a method of dissecting a wave mode into its traveling and standing parts is also proposed from the complex modes and modal coordinates frequencies wavelengths and characteristic wave speeds can be obtained the method is applied to traveling and standing wave examples

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

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

small amplitude solutions of the generalized imbq equation in this paper the global existence of small amplitude solution for the cauchy problem of the multidimensional generalized imbq equation is proved moreover we obtain a nonlinear scattering result of the cauchy problem of the imbq equation for small initial data

well posedness in energy space for the periodic modified benjamin ono equation abstract we prove that the periodic modified benjamin ono equation is locally well posed in the energy space h 1 2 this ensures the global well posedness in the defocusing case the proof is based on an x s b analysis of the system after a gauge transform

image denoising by sparse 3 d transform domain collaborative filtering we propose a novel image denoising strategy based on an enhanced sparse representation in transform domain the enhancement of the sparsity is achieved by grouping similar 2d image fragments e g blocks into 3d data arrays which we call groups collaborative altering is a special procedure developed to deal with these 3d groups we realize it using the three successive steps 3d transformation of a group shrinkage of the transform spectrum and inverse 3d transformation the result is a 3d estimate that consists of the jointly filtered grouped image blocks by attenuating the noise the collaborative filtering reveals even the finest details shared by grouped blocks and at the same time it preserves the essential unique features of each individual block the filtered blocks are then returned to their original positions because these blocks are overlapping for each pixel we obtain many different estimates which need to be combined aggregation is a particular averaging procedure which is exploited to take advantage of this redundancy a significant improvement is obtained by a specially developed collaborative wiener filtering an algorithm based on this novel denoising strategy and its efficient implementation are presented in full detail an extension to color image denoising is also developed the experimental results demonstrate that this computationally scalable algorithm achieves state of the art denoising performance in terms of both peak signal to noise ratio and subjective visual quality

multifractal analysis of a lobed mixer flowfield utilizing the proper orthogonal decomposition we use the theory of multifractal measures to throw a fresh perspective on the data analysis of velocity time traces in a lobed mixer flow a lobed mixer is a device that enhances mixing through secondary flows and streamwise vorticity a specially designed rake of hot wires with high spatial resolution was used to collect the streamwise velocity data through the use of the proper orthogonal decomposition a basic knowledge of the coherent structures on an energy weighted basis was studied the instantaneous velocity traces that are necessary for calculating the generalized fractal dimensions are reproduced from the ensemble average measurements taken from the proper orthogonal decomposition we compute the generalized fractal dimensions dq and the a multifractal spectrum of several proper eigenmodes for data samples from the velocity time trace of several hot wire probes at different energy levels this is a marked departure from previous multifractal theory applications to self similar cascades that mainly dealt with the dissipation fields of turbulent kinetic energy in the course of this exposition it will be pointed out that in certain cases a single dimension d may suffice to capture the entire spectrum of scaling exponents for the velocity time trace we verify that in such cases the location of the hot wire probes imply a lack of intermittency

on blow up criteria of smooth solutions to the 3 d euler equations in a bounded domain abstract we show that a smooth solution of the 3 d euler equations in a bounded domain breaks down if and only if a certain norm of vorticity blows up at the same time here this norm is weaker than bmo norm

well posedness of the water waves equations 1 1 presentation of the problem the water waves problem for an ideal liquid consists of describing the motion of the free surface and the evolution of the velocity field of a layer of perfect incompressible irrotational fluid under the influence of gravity in this paper we restrict our attention to the case when the surface is a graph parameterized by a function x where t denotes the time variable and x xi xd rd the horizontal spatial variables the method developed here works equally well for any integer d 1 but the only physically relevant cases are of course d 1 and d 2 the layer of fluid is also delimited from below by a not necessarily flat bottom parameterized by a time independent function b x we denote by q t the fluid domain at time t the incompressibility of the fluids is expressed by 1 1 div v 0 in qu t 0

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

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

interior jump and piecewise regularity for compressible stokes equations in the t shaped cavity domain abstract in the t shaped cavity domain the fluid flows consist of three essential phenomena that are the flows in the top region with inflow and outflow the ones in the bottom cavity region and the interface fluctuation between two flows we consider a simple modeling problem of compressible stokes flows to illustrate them the domain is split by the interior curve connecting the upstream and downstream corners the transport equation is directed by the vector field having jump discontinuity with respect to the curve so the continuity equation shows the pressure jump solution across the curve and the velocity vector by the momentum equations has the singular behaviors due to the pressure gradient plus the corner singularities at the non convex corners we establish a piecewise maximal regularity by constructing a vector function corresponding to the pressure jump on the interior curve without subtracting the corner singularities

a regularity criterion for the solution of nematic liquid crystal flows in terms of the b 1 norm abstract in this paper we investigate the regularity criterion for the solution of nematic liquid crystal flows in three dimensions n 3 and in two dimensions n 2 we prove that the solution u d is smooth up to time t provided that there exists a positive constant e 0 0 such that i for n 3 u d l 0 t b 1 e 0 and ii for n 2 d l 0 t b 1 e 0

eigenfunction analysis of turbulent mixing phenomena this paper has focused on the problem of mixing and mixing assessment the k l procedure applied to data collected from a jet in crossflow provides optimal bases for the analysis of the flow it is found that better mixed flows are characterized by the dominance of spatially complex eigenfunctions qualitative measures of the complexity are presented and it is anticipated that this technique will provide a sensitive metric of the mixedness of flows in a wide variety of applications

contour based object detection as dominant set computation contour based object detection can be formulated as a matching problem between model contour parts and image edge fragments we propose a novel solution by treating this problem as the problem of finding dominant sets in weighted graphs the nodes of the graph are pairs composed of model contour parts and image edge fragments and the weights between nodes are based on shape similarity because of high consistency between correct correspondences the correct matching corresponds to a dominant set of the graph consequently when a dominant set is determined it provides a selection of correct correspondences as the proposed method is able to get all the dominant sets we can detect multiple objects in an image in one pass moreover since our approach is purely based on shape we also determine an optimal scale of target object without a common enumeration of all possible scales both theoretic analysis and extensive experimental evaluation illustrate the benefits of our approach

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

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