well posedness for the schrodinger korteweg de vries system we study well posedness of the cauchy problem associated to the schrodinger korteweg de vries system we obtain local well posedness for weak initial data where the best result obtained is for data in the sobolev space l 2 r x h 3 4 this result implies in particular the global well posedness in the energy space h 1 r x h 1 r both results considerably improve the previous ones by bekiranov ogawa and ponce 1997 guo and miao 1999 and tsutsumi 1993

some remarks on the blow up rate for the 3d magnetic zakharov system we continue our study 8 on the cauchy problem for the three dimensional magnetic zakharov system zsm iet e ne i e b e 0 nt v vt n e 2 b i e e b 0 with initial data zsm 1 e 0 x e0 x n 0 x n0 x v 0 x v0 x let e n v c 0 t h1 r3 l2 r3 l2 r3 be a blow up solution to the cauchy problem zsm zsm 1 and let t be its blow up time then e n satisfies the space time integral estimate e 1 0t r3 n t x qdx 1q r3 e t x 2qdx 1q dt where 1e e 0 14 and q 32 1 e 32 2 the estimate e 1 implies that for a 1 supt 0 t t t ae n t lq r3 e t l2q r3 2 in particular if e n v is a radially symmetric solution to zsm zsm 1 then supt 0 t t t ae n t lq d e t l2q d 2 where a 0 13 and d x r3 x 1

stability and approximation for a linear viscoelastic model we consider an integro differential equation which arises in linear viscoelasticity by making use of an equivalent inner product it is shown that the underlying contraction semigroup is exponentially stable we also show that the finite dimensional semigroups arising from a known approximation scheme are uniformly exponentially stable

on the periodic schrodinger boussinesq system abstract we study the local and global well posedness of the periodic boundary value problem for the nonlinear schrodinger boussinesq system the existence of periodic traveling wave solutions as well as the orbital stability of such solutions are also considered

control and stabilization of the benjamin ono equation in l 2 mathbb t we study the control and stabilization of the benjamin ono equation in l 2 mathbb t the lowest regularity where the initial value problem is well posed this problem was already initiated in linares and rosier trans am math soc 367 4595 4626 2015 where a stronger stabilization term was used that makes the equation of parabolic type in the control zone here we employ a more natural stabilization term related to the l2 norm moreover by proving a theorem of controllability in l2 we manage to prove the global controllability in large time our analysis relies strongly on the bilinear estimates proved in molinet and pilod anal pde 5 365 395 2012 and some new extension of these estimates established here

a bit allocation method for sparse source coding in this paper we develop an efficient bit allocation strategy for subband based image coding systems more specifically our objective is to design a new optimization algorithm based on a rate distortion optimality criterion to this end we consider the uniform scalar quantization of a class of mixed distributed sources following a bernoulli generalized gaussian distribution this model appears to be particularly well adapted for image data which have a sparse representation in a wavelet basis in this paper we propose new approximations of the entropy and the distortion functions using piecewise affine and exponential forms respectively because of these approximations bit allocation is reformulated as a convex optimization problem solving the resulting problem allows us to derive the optimal quantization step for each subband experimental results show the benefits that can be drawn from the proposed bit allocation method in a typical transform based coding application

on global existence for the schrodinger ib system abstract in this paper we study global well posedness of the schrodinger improved boussinesq s ib system of equations in sobolev spaces we prove that the one and two dimensional s ib systems are globally well posed in l 2 r h 1 2 r h 1 2 r and l 2 r 2 l 2 r 2 l 2 r 2 h 1 r 2 respectively improving the corresponding results of ozawa and tsutaya t ozawa k tsutaya on the cauchy problem for schrodinger improved boussinesq equations adv stud pure math in press

asymptotic behavior of the eigenfrequency of a one dimensional linear thermoelastic system abstract in this paper we are concerned with the asymptotic behavior of the eigenvalues arising from a one dimensional linear thermoelastic system with the dirichlet dirichlet boundary condition it is shown that the eigenfrequency asymptotically falls on two branches one branch is along the negative horizontal axis in the complex plane and the other branch is asymptotic to the vertical line re 2 2k these results lead to the exponential stability of the system and also provide a proof for the numerical simulation results by 1

a numerical model for the raman amplification for laser plasma interaction in this paper we continue the study of the raman amplification initiated in m colin t colin on a quasi linear zakharov system describing laser plasma interactions differential integral equations 17 3 4 2004 297 330 we use a dispersive quasi linear system the quasi linear part is not hyperbolic and this difficulty is overcome using the dispersion we give an asymptotic result on a reduced system we then introduce a simple robust and efficient numerical scheme on the whole system that takes into account the non hyperbolicity of the quasi linear part as well as the nonlinear saturation of the raman growth the scheme is validated thanks to the asymptotic result finally we present 1 d and 2 d simulations

interaction equations for short and long dispersive waves abstract we show the time local well posedness for a system of nonlinear dispersive equations for the water wave interaction formula it is shown that for any initial data u0 v0 hs r hs 1 2 r s 0 the solution for the above equation uniquely exists in a subset ofc t t hs c t t hs 1 2 and depends continuously on the data by virtue of a special structure of the nonlinear coupling the solution is stable under a singular limiting process

generalized strichartz estimates and scattering for 3d zakharov system we obtain scattering for the 3d zakharov system with non radial small data in the energy space with angular regularity of degree one the main ingredient is a generalized strichartz estimate for the schrodinger equation in the space of l2 angular integrability

blowup result for a type of generalized zakharov system abstract we study the blowup for a type of generalized zakharov system in this paper it is proved that the solution of such system either blows up in finite time or blows up in infinite time provided that the initial energy is negative

wellposedness for semirelativistic schrodinger equation with power type nonlinearity abstract in this paper we employ bourgain type norm to investigate the wellposedness for the cauchy problem of one dimensional semirelativistic schrodinger equation with cubic nonlinearity in space h s we extend the previous existence result to the space regularity s 1 4 moreover we point out the persistence of the solution in different regularity space is uniform by an iterate argument additionally we are also able to say more for semirelativistic schrodinger equation with general power type nonlinearity

analysis of low bit rate image transform coding calculations based on high resolution quantizations prove that the distortion rate d r of an image transform coding is proportional to 2 sup 2r when r is large enough in wavelet and block cosine bases we show that if r 1 bit pixel then d r varies like r sup 1 2 spl gamma where spl gamma remains of the order of 1 for most natural images the improved performance of embedded codings in wavelet bases is analyzed at low bit rates we show that the compression performance of an orthonormal basis depends mostly on its ability to approximate images with a few nonzero vectors

on the cauchy problem for the generalized shallow water wave equation abstract in this paper we mainly study the cauchy problem for the generalized shallow water wave equation in the sobolev space h s of lower order s using the crucial bilinear estimates in the fourier transform restriction spaces related to the shallow water wave equation we establish local well posedness in h s with any s 11 16

local well posedness for the sixth order boussinesq equation abstract in this work we study the local well posedness of the initial value problem for the nonlinear sixth order boussinesq equation u t t u x x u x x x x u x x x x x x u 2 x x where 1 we prove the local well posedness with initial data in non homogeneous sobolev spaces h s r for negative indices of s r

entropy based evaluation of context models for wavelet transformed images entropy is a measure of a message uncertainty among others aspects it serves to determine the minimum coding rate that practical systems may attain this paper defines an entropy based measure to evaluate context models employed in wavelet based image coding the proposed measure is defined considering the mechanisms utilized by modern coding systems it establishes the maximum performance achievable with each context model this helps to determine the adequateness of the model under different coding conditions and serves to predict with high precision the coding rate achieved by practical systems experimental results evaluate four well known context models using different types of images coding rates and transform strategies they reveal that under specific coding conditions some widely spread context models may not be as adequate as it is generally thought the hints provided by this analysis may help to design simpler and more efficient wavelet based image codecs

supersonic limit for the zakharov rubenchik system abstract we study the asymptotic behavior of the solutions of zakharov rubenchik system when appropriate parameters go to zero namely we state weak and strong convergence results of these solutions to solutions of zakharov system the proof of the weak limit is a classical argument in the theory of compactness whose main ingredient is the aubin lions theorem and the ascoli theorem strong limits are conveniently treated by decomposing the nonlinearities and using the strichartz estimates associated with the group of the schrodinger equation and the wave group

local well posedness of the ostrovsky stepanyams and tsimring equation in sobolev spaces of negative indices abstract in this paper we prove by using the method of bilinear estimate in the bourgain type spaces that the initial value problem of the ost equation u t u x x x h u x h u x x x u u x 0 x r t 0 where 0 and h denotes the usual hilbert transformation is locally well posed in the sobolev space h s r when s 1

on the low regularity of the benney lin equation abstract we consider the low regularity of the benney lin equation u t u u x u x x x u x x u x x x x u x x x x x 0 we established the global well posedness for the initial value problem of benney lin equation in the sobolev spaces h s r for 0 s 2 improving the well posedness result of biagioni and linares h a biaginoi f linares on the benney lin and kawahara equation j math anal appl 211 1997 131 152 for s 2 we also prove some ill posedness issues

generalized strichartz inequalities for the wave equation strichartz inequalities for the wave equation u f are estimates of the solution u of the cauchy problem for that equation in the form of space time integral norms in terms of similar norms of the inhomogeneity f and of suitable norms of the initial data

global existence for 2d nonlinear schrodinger equations via high low frequency decomposition method abstract we study global existence of solutions for the cauchy problem of the nonlinear schrodinger equation i u t u u 2 m u in the 2 dimension case where m is a positive integer m 2 using the high low frequency decomposition method we prove that if 10 m 6 10 m 5 s 1 then for any initial value h s r 2 the cauchy problem has a global solution in c r h s r 2 and it can be split into u t e i t y t with y c r h 1 r 2 satisfying y t h 1 1 t 2 1 s 10 m 5 s 10 m 6 where is an arbitrary sufficiently small positive number

an improved local well posedness result for the one dimensional zakharov system abstract the 1d cauchy problem for the zakharov system is shown to be locally well posed for low regularity schrodinger data u 0 h k p and wave data n 0 n 1 h l p h l 1 p under certain assumptions on the parameters k l and 1 p 2 where u 0 h k p k u 0 l p generalizing the results for p 2 by ginibre tsutsumi and velo especially we are able to improve the results from the scaling point of view and also allow suitable k 0 l 1 2 i e data u 0 l 2 and n 0 n 1 h 1 2 h 3 2 which was excluded in the case p 2

the electrostatic limit for the 3d zakharov system abstract we consider the vectorial zakharov system describing langmuir waves in a weakly magnetized plasma in its original derivation zakharov 1972 the evolution for the electric field envelope is governed by a schrodinger type equation with a singular parameter which is usually large in physical applications motivated by this we study the rigorous limit as this parameter goes to infinity by using some strichartz type estimates to control separately the fast and slow dynamics in the problem we show that the evolution of the electric field envelope is asymptotically constrained onto the space of irrotational vector fields

global well posedness in l 2 for the periodic benjamin ono equation we prove that the benjamin ono equation is globally well posed in h s bbb t for s ge 0 moreover we show that the associated flow map is lipschitz on every bounded set of h s 0 bbb t s ge 0 and even real analytic in this space for small times this result is sharp in the sense that the flow map if it can be defined and coincides with the standard flow map on h 0 infty bbb t cannot be of class c 1 alpha alpha 0 from h 0 s bbb t into h 0 s bbb t as soon as s 0

space propagation of instabilities in zakharov equations in this paper we study an initial boundary value problem for the zakharov equations describing the space propagation of a laser beam entering a plasma we prove a strong instability result and prove that the mathematical problem is ill posed in sobolev spaces we also show that it is well posed in spaces of analytic functions several consequences for the physical consistency of the model are discussed

on the zakharov and zakharov schulman systems abstract we consider the initial value problem for the zakharov system formula which models the long wave langmuir turbulence in a plasma using the standard iteration scheme in the original system it is shown that the system is locally well posed uniformly on the ionic speed of sound in appropriate sobolev spaces the method provides similar results for the ivp for the zakharov schulman system formula where u r d 0 c r d 0 r and formula with a i j k a k i j real constants which models the interactions of small amplitude high frequency waves with acoustic type waves

well posedness for the cauchy problem associated to a periodic boussinesq equation abstract we consider the initial value problem associated to the nonlinear periodic sixth order boussinesq equation for given initial data in sobolev spaces h s t the local well posedness of this equation is established for s 1 2

on the convergence of the solution for a generalized zakharov system in this paper we study the limit behavior of the smooth solution for the generalized zakharov system with a magnetic field which describes the spontaneous generation of a magnetic field in a cold plasma by showing uniform bounds of solutions for this system with suitable initial data we prove that solution of the generalized zakharov system converges to the solution of the nonlinear schrodinger equation with a magnetic field

on a perturbation of the benjamin ono equation abstract we prove using the fourier restriction norm method that the initial value problem associated to a perturbation of the benjamin ono equation u t u u x h u x x h u x u x x 0 where x r t 0 0 and h denotes the usual hilbert transform is locally well posed in the sobolev space h s r for any s 1 2 and globally well posed in h s r when s 0 for s 1 we also prove some ill posedness issues

wavelet based texture retrieval using generalized gaussian density and kullback leibler distance we present a statistical view of the texture retrieval problem by combining the two related tasks namely feature extraction fe and similarity measurement sm into a joint modeling and classification scheme we show that using a consistent estimator of texture model parameters for the fe step followed by computing the kullback leibler distance kld between estimated models for the sm step is asymptotically optimal in term of retrieval error probability the statistical scheme leads to a new wavelet based texture retrieval method that is based on the accurate modeling of the marginal distribution of wavelet coefficients using generalized gaussian density ggd and on the existence a closed form for the kld between ggds the proposed method provides greater accuracy and flexibility in capturing texture information while its simplified form has a close resemblance with the existing methods which uses energy distribution in the frequency domain to identify textures experimental results on a database of 640 texture images indicate that the new method significantly improves retrieval rates e g from 65 to 77 compared with traditional approaches while it retains comparable levels of computational complexity

information theoretic analysis of interscale and intrascale dependencies between image wavelet coefficients this paper presents an information theoretic analysis of statistical dependencies between image wavelet coefficients the dependencies are measured using mutual information which has a fundamental relationship to data compression estimation and classification performance mutual information is computed analytically for several statistical image models and depends strongly on the choice of wavelet filters in the absence of an explicit statistical model a method is studied for reliably estimating mutual information from image data the validity of the model based and data driven approaches is assessed on representative real world photographic images our results are consistent with empirical observations that coding schemes exploiting inter and intrascale dependencies alone perform very well whereas taking both into account does not significantly improve coding performance a similar observation applies to other image processing applications

sharp bilinear estimates and its application to a system of quadratic derivative nonlinear schrodinger equations abstract in the present paper we consider the cauchy problem of the system of quadratic derivative nonlinear schrodinger equations for the spatial dimension d 2 and 3 this system was introduced by colin and colin 2004 the first author obtained some well posedness results in the sobolev space h s but under some condition for the coefficient of laplacian this result is not optimal we improve the bilinear estimate by using a nonlinear version of the classical loomis whitney inequality and prove well posedness in h s for s 1 2 if d 2 and s 1 2 if d 3

the well posedness of the dissipative korteweg de vries equations with low regularity data abstract we study the cauchy problem of a dissipative version of the kdv equation with rough initial data by working in a bourgain type space we prove the local and global well posedness results for sobolev spaces of negative order and the order number is lower than the well known value 3 4 in some sense this paper is intended to show how the bourgain type space is applicable to the study of semilinear equations with a linear part which contain both dissipative and dispersive terms

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

low regularity global well posedness for the zakharov and klein gordon schrodinger systems we prove low regularity global well posedness for the id zakharov system and the 3d klein gordon schrodinger system which are systems in two variables u r d x x r t c and n r d x x r t r the zakharov system is known to be locally well posed in u n l 2 x h and the klein gordon schrodinger system is known to be locally well posed in u n l 2 x l 2 here we show that the zakharov and klein gordon schrodinger systems are globally well posed in these spaces respectively by using an available conservation law for the l 2 norm of u and controlling the growth of n via the estimates in the local theory

decay of solutions of wave equations in a bounded region with boundary dissipation abstract an energy decay rate is obtained for solutions of wave type equations in a bounded region in rn whose boundary consists partly of a nontrapping reflecting surface and partly of an energy absorbing surface

comparison of numerical methods for the zakharov system in the subsonic limit regime abstract we compare numerically spatial temporal resolution of various methods for solving the zakharov system zs in the subsonic limit regime which involves a small parameter 0 e 1 inversely proportional to the acoustic speed in this regime i e 0 e 1 the solution presents highly oscillatory initial layers due to the wave operator or the incompatibility of the initial data specifically the solution propagates waves with wavelength of o e and o 1 in time and space respectively by applying the sine pseudospectral discretization for spatial derivatives followed by a time splitting technique for integrating the schrodinger equation combined with an exponential wave integrator in phase space for integrating the wave equation we propose four different numerical methods for the zs based on different quadrature rules for approximating the integral or some property of conservation numerical results suggest that all the methods are spectrally accurate in space which is uniformly for e 0 1 for temporal error the best method converges uniformly with linear convergence rate at o in the subsonic limit regime

comparison of different methods of classification in subband coding of images this paper investigates various classification techniques applied to subband coding of images as a way of exploiting the nonstationary nature of image subbands the advantages of subband classification are characterized in a rate distortion framework in terms of classification gain and overall subband classification gain two algorithms maximum classification gain and equal mean normalized standard deviation classification which allow unequal number of blocks in each class are presented the dependence between the classification maps from different subbands is exploited either directly while encoding the classification maps or indirectly by constraining the classification maps the trade off between the classification gain and the amount of side information is explored coding results for a subband image coder based on classification are presented the simulation results demonstrate the value of classification in subband coding

optimal lower bound estimates for the blow up rate for the zakharov system in a nonhomogeneous medium abstract in this paper we obtain lower bound estimates for the blow up rate of finite time blow up solutions to the cauchy problem for the zakharov system in a nonhomogeneous medium in two space dimensions by introducing suitable scale transformations of space and time and the use of compactness arguments we derive an optimal lower bound estimate in the energy space h 2 r 2 l 2 r 2 h 1 r 2 for the blow up rate for t near the finite blow up time t also we give an application to the virial identity for the zakharov system under study

on the cauchy problem for the zakharov system abstract we study the local cauchy problem in time for the zakharov system 1 1 and 1 2 governing langmuir turbulence with initial data u 0 n 0 t n 0 h k h lscr h l 1 in arbitrary space dimension we define a natural notion of criticality according to which the critical values of k l are 2 3 2 2 2 using a method recently developed by bourgain we prove that the zakharov system is locally well posed for a variety of values of k l the results cover the whole subcritical range for 4 for 3 they cover only part of it and the lowest admissible values are k l 1 2 0 for 2 3 and k l 0 1 2 for 1 as a by product of the one dimensional result we prove well posedness of the benney system 1 14 and 1 15 governing the interaction of short and long waves for the same values of k l

blow up and nonlinear instability for the magnetic zakharov system abstract this study deals with the generalized zakharov system with magnetic field first of all we construct a kind of blow up solutions and establish the existence of blow up solutions to the system through considering an elliptic system next we show the nonlinear instability for a kind of periodic solutions in addition we consider the concentration properties of blow up solutions for the system under study at the end of this paper we establish the global existence of weak solutions to the cauchy problem of the system under consideration

visibility of wavelet quantization noise the discrete wavelet transform dwt decomposes an image into bands that vary in spatial frequency and orientation it is widely used for image compression measures of the visibility of dwt quantization errors are required to achieve optimal compression uniform quantization of a single band of coefficients results in an artifact that we call dwt uniform quantization noise it is the sum of a lattice of random amplitude basis functions of the corresponding dwt synthesis filter we measured visual detection thresholds for samples of dwt uniform quantization noise in y cb and cr color channels the spatial frequency of a wavelet is r2 sup spl lambda where r is the display visual resolution in pixels degree and spl lambda is the wavelet level thresholds increase rapidly with wavelet spatial frequency thresholds also increase from y to cr to cb and with orientation from lowpass to horizontal vertical to diagonal we construct a mathematical model for dwt noise detection thresholds that is a function of level orientation and display visual resolution this allows calculation of a perceptually lossless quantization matrix for which all errors are in theory below the visual threshold the model may also be used as the basis for adaptive quantization schemes

efficient entropy estimation based on doubly stochastic models for quantized wavelet image data under a rate constraint wavelet based image coding involves strategic discarding of information such that the remaining data can be described with a given amount of rate in a practical coding system this task requires knowledge of the relationship between quantization step size and compressed rate for each group of wavelet coefficients the r q curve a common approach to this problem is to fit each subband with a scalar probability distribution and compute entropy estimates based on the model this approach is not effective at rates below 1 0 bits per pixel because the distributions of quantized data do not reflect the dependencies in coefficient magnitudes these dependencies can be addressed with doubly stochastic models which have been previously proposed to characterize more localized behavior though there are tradeoffs between storage computation time and accuracy using a doubly stochastic generalized gaussian model it is demonstrated that the relationship between step size and rate is accurately described by a low degree polynomial in the logarithm of the step size based on this observation an entropy estimation scheme is presented which offers an excellent tradeoff between speed and accuracy after a simple data gathering step estimates are computed instantaneously by evaluating a single polynomial for each group of wavelet coefficients quantized with the same step size these estimates are on average within 3 of a desired target rate for several of state of the art coders

uniform exponential stability and approximation in control of a thermoelastic system this paper has two objectives first necessary and sufficient conditions are given to characterize the uniform exponential stability of a sequence of c 0 semigroups t n t on hilbert space h n secondly approximation in control of a one dimensional thermoelastic system subject to dirichlet dirichlet as well as dirichlet neumann boundary conditions is considered the uniform exponential stability and strong convergence of corresponding semigroups associated with approximate scheme are proved numerical experimental results are also presented

on the modeling of dct and subband image data for compression image subband and discrete cosine transform coefficients are modeled for efficient quantization and noiseless coding quantizers and codes are selected based on laplacian fixed generalized gaussian and adaptive generalized gaussian models the quantizers and codes based on the adaptive generalized gaussian models are always superior in mean squared error distortion performance but generally by no more than 0 08 bit pixel compared with the much simpler laplacian model based quantizers and noiseless codes this provides strong motivation for the selection of pyramid codes for transform and subband image coding

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 the low regularity of the fifth order kadomtsev petviashvili i equation we consider the fifth order kadomtsev petviashvili i kp i equation as tu 3 x u 5 x u 1 x 2 y u uux 0 while r we introduce an interpolated energy space es to consider the well posedeness of the initial value problem ivp of the fifth order kp i equation we obtain the local well posedness of ivp of the fifth order kp i equation in es for 0 s 1 to obtain the local well posedness we present a bilinear estimate in the bourgain space in the framework of the interpolated energy space it crucially depends on the dyadic decomposed strichartz estimate the fifth order dispersive smoothing effect and maximal estimate

local well posedness for the modified kdv equation in almost critical widehat h r_s spaces we study the cauchy problem for the modified kdv equation u t u xxx u 3 x 0 u 0 u 0 for data u 0 in the space h r s defined by the norm u 0 h r s s u 0 lr local well posedness of this problem is established in the parameter range 2 r 1 s 1 2 1 2r so the case s r 0 1 which is critical in view of scaling considerations is almost reached to show this result we use an appropriate variant of the fourier restriction norm method as well as bi and trilinear estimates for solutions of the airy equation

global dynamics below the ground state energy for the zakharov system in the 3d radial case abstract we consider the global dynamics below the ground state energy for the zakharov system in the 3d radial case we obtain dichotomy between the scattering and the growup

on the uniform quantization of a class of sparse sources we consider the uniform scalar quantization of a class of mixed distributed memoryless sources namely sources having a bernoulli generalized gaussian bgg distribution both for low and high resolutions asymptotic expressions of the distortion for a pth order moment error measure and close approximations of the entropy are provided for these sources operational rate distortion functions at high bit rate and their slope factors at low bit rate are derived the dependence of these results on p and the distribution parameters as well as the relation to the shannon optimal rate distortion bound are then discussed the application of these results to transform coding in two simple cases is finally highlighted

local and global well posedness for the 2d zakharov kuznetsov burgers equation in low regularity sobolev space abstract in the present paper we consider the cauchy problem of the 2d zakharov kuznetsov burgers zkb equation which has the dissipative term x 2 u this is known that the 2d zakharov kuznetsov equation is well posed in h s r 2 for s 1 2 and the 2d nonlinear parabolic equation with quadratic derivative nonlinearity is well posed in h s r 2 for s 0 by using the fourier restriction norm with dissipative effect we prove the well posedness for zkb equation in h s r 2 for s 1 2

soliton solutions and chaotic motions for the 2 1 dimensional zakharov equations in a laser induced plasma the 2 1 dimensional zakharov equations arising from the propagation of a laser beam in a plasma are studied in this paper analytic soliton solutions are obtained by means of the symbolic computation based on which we find that e is inversely related to p e but positively related to m i and c s while n is inversely related to p e and l but positively related to n 0 with e as the envelope of the high frequency electric field n as the plasma density while p e l n 0 m i and c s as the plasma electronic frequency frequency of the laser beam mean density of the plasma mass of an ion and ion sound velocity in the plasma respectively head on interaction is found to be transformed into an overtaking one with p e increasing or n 0 decreasing also period of the bound state interaction decreases with l decreasing considering the driving forces in the laser induced plasma we explore the associated chaotic motions as well as the effects of l p e k l n 0 m i c s f 1 and f 2 where k l is the wave number of the laser beam f 1 and f 1 represent the frequencies of driving forces respectively it is found that the chaotic motions can be weakened with p e c s and f 1 increasing or with n 0 m i and f 2 decreasing and the periodic motion can occur when f 1 reaches the critical value 2 while the chaotic motions are independent of l and k l

equations of langmuir turbulence and nonlinear schrodinger equation smoothness and approximation we consider the following family of systems parametrized by e 0 which describe langmuir s turbulence in the case where initial data are sufficiently small we study the asymptotic behaviour of the solutions ee ne when e goes to zero for d 1 2 3 namely we state convergence results of ee ne to the couple e e 2 where e is the solution of the nonlinear schrodinger equation moreover in three dimensions we show that the smooth solution ee ne is defined on 0 tmax e with tmax e going to infinity as e goes to 0

exponential energy decay in a linear thermoelastic rod abstract we examine the stability of solutions to a pair of coupled linear partial differential equations which describe the temperature distribution and displacement within a one dimensional thermoelastic rod for particular sets of natural boundary conditions the eigenfunctions are shown to form a riesz basis on the hilbert space of finite energy states for these cases asymptotic eigenvalue estimates show that the spectrum is to the left of some vertical line re contained in the open left half of the complex plane an energy decay estimate of the form e t me t e 0 is then obtained

well posedness for the cauchy problem for a system of semirelativistic equations the local well posedness for the cauchy problem of a system of semirelativistic equations in one space dimension is shown in the sobolev space hs of order s 0 we apply the standard contraction mapping theorem by using bourgain type spaces xs b we also use an auxiliary space for the solution in l2 h0 we give the global well posedness by this conservation law and the argument of the persistence of regularity

low regularity bilinear estimates for a quadratic nonlinear schrodinger equation abstract in this article we establish the bilinear estimates corresponding to the 1d and 2d nls with a quadratic nonlinearity c 1 u 2 c 2 u 2 which imply the local well posedness of the cauchy problem in h s for s 1 in the 1d case and for s 1 in the 2d case this is a continuation of our study n kishimoto local well posedness for the cauchy problem of the quadratic schrodinger equation with nonlinearity u 2 commun pure appl anal 7 2008 1123 1143 on the 1d nls with nonlinearity c u 2 previous papers by kenig ponce and vega and colliander delort kenig and staffilani established local well posedness for s 3 4 in 1d and in 2d respectively and when the nonlinearity is restricted to c u 2 papers by bejenaru and tao and bejenaru and de silva improved these results to s 1 in 1d and s 1 in 2d the bilinear estimate for 2d also yields an improvement on the growth rate of sobolev norms of finite energy global in time solutions to the 2d cubic nls

quasi invariant gaussian measures for the cubic fourth order nonlinear schrodinger equation we consider the cubic fourth order nonlinear schrodinger equation on the circle in particular we prove that the mean zero gaussian measures on sobolev spaces h s mathbb t s frac 3 4 are quasi invariant under the flow

image compression via joint statistical characterization in the wavelet domain we develop a probability model for natural images based on empirical observation of their statistics in the wavelet transform domain pairs of wavelet coefficients corresponding to basis functions at adjacent spatial locations orientations and scales are found to be non gaussian in both their marginal and joint statistical properties specifically their marginals are heavy tailed and although they are typically decorrelated their magnitudes are highly correlated we propose a markov model that explains these dependencies using a linear predictor for magnitude coupled with both multiplicative and additive uncertainties and show that it accounts for the statistics of a wide variety of images including photographic images graphical images and medical images in order to directly demonstrate the power of the model we construct an image coder called epwic embedded predictive wavelet image coder in which subband coefficients are encoded one bitplane at a time using a nonadaptive arithmetic encoder that utilizes conditional probabilities calculated from the model bitplanes are ordered using a greedy algorithm that considers the mse reduction per encoded bit the decoder uses the statistical model to predict coefficient values based on the bits it has received despite the simplicity of the model the rate distortion performance of the coder is roughly comparable to the best image coders in the literature

on a local energy decay estimate of solutions to the hyperbolic type stokes equations abstract in this paper we discuss a local energy decay estimate of solutions to the initial boundary value problem for the hyperbolic type stokes equations of incompressible fluid flow in an exterior domain and a perturbed half space the equations are linearized version of the hyperbolic navier stokes equations introduced by racke and saal 15 which are obtained as a delayed case for the deformation tensor in the incompressible navier stokes equations our proof of the local energy decay estimate is based on dan and shibata 2 in 2 they treated the dissipative wave equations in an exterior domain and discussed the local energy decay estimate our approach uses the fact that applying the helmholtz projection to the hyperbolic type stokes equations we obtain equations similar to the dissipative wave ones

global solutions of the derivative schrodinger equation in a class of functions analytic in a strip lower bounds on the rate of decrease in time of a uniform radius of spatial analyticity for solutions of the derivative schrodinger equation are derived the bounds depend algebraically on time they are valid as long as the initial datum is of order one in l2 norm and satisfies suitable spatial decay requirements on the real axis

the cauchy problem for higher order kp equations abstract we study the local well posedness of higher order kp equations our well posedness results make an essential use of a global smoothing effect for the linearized equation established in ben artzi and saut preprint 1997 injected into the framework of fourier transform restriction spaces introduced by bourgain our ill posedness results rely on the existence of solitary wave solutions and on scaling arguments the method was first applied in the context of the kdv and schrodinger equations cf birnir et al ann inst h poincare anal non lineaire 13 1996 529 535 birnir et al j london math soc 53 1996 551 559

sharp ill posedness result for the periodic benjamin ono equation abstract we prove the discontinuity for the weak l 2 t topology of the flow map associated with the periodic benjamin ono equation this ensures that this equation is ill posed in h s t as soon as s 0 and thus completes exactly the well posedness result obtained in molinet 2008 12

cauchy problem of schrodinger improved boussinesq systems on the torus in this paper we will study the local well posedness of schrodinger improved boussinesq system with additive noise in td d 1 and we will also study the global well posedness of dimension 1 case with the initial data u0 v1 v2 l2 l2 l2 almost surely gaining some exponential growth of l2 norm of v

derivation of the zakharov equations this article continues the study initiated in 27 7 of the validity of the zakharov model which describes langmuir turbulence we give an existence theorem for a class of singular quasilinear equations this theorem is valid for prepared initial data we apply this result to the euler maxwell equations which describes laser plasma interactions to obtain in a high frequency limit an asymptotic estimate that describes solutions of the euler maxwell equations in terms of wkb approximate solutions the leading terms of which are solutions of the zakharov equations due to the transparency properties of the euler maxwell equations evidenced in 27 this study is carried out in a supercritical highly nonlinear regime in such a regime resonances between plasma waves electromagnetric waves and acoustic waves could create instabilities in small time the key of this work is the control of these resonances the proof involves the techniques of geometric optics of joly metivier and rauch 12 13 recent results by lannes on norms of pseudodifferential operators 14 and a semiclassical paradifferential calculus

on the low regularity of the modified korteweg de vries equation with a dissipative term abstract we consider a dissipative version of the modified korteweg de vries equation u t u x x x u x x u 3 x 0 we prove global well posedness results on the associated cauchy problem in the sobolev spaces h s r for s 1 4 while for s 1 2 we prove some ill posedness issues

on the existence and uniqueness of smooth solution for a generalized zakharov equation abstract the paper deals with the existence and uniqueness of smooth solution for a generalized zakharov equation we establish local in time existence and uniqueness in the case of dimension d 2 3 moreover by using the conservation laws and brezis gallouet inequality the solution can be extended globally in time in two dimensional case for small initial data besides we also prove global existence of smooth solution in one spatial dimension without any small assumption for initial data

global solutions of the klein gordon schrodinger system with rough data in r 2 1 abstract in this paper we consider the klein gordon schrodinger system with quadratic yakuwa coupling and cubic autointeractions in r 2 1 and prove the existence and uniqueness of global solution for rough data the techniques to be used are adapted from a general scheme originally introduced by j bourgain to split the data into the low and high frequency parts

well posedness and weak rotation limit for the ostrovsky equation we consider the cauchy problem of the ostrovsky equation we first prove the time local well posedness in the anisotropic sobolev space hs a with s a 2 3 4 and 0 a 1 by the fourier restriction norm method this result include the time local well posedness in hs with s 3 4 for both positive and negative dissipation namely for both 0 and 0 we next consider the weak rotation limit we prove that the solution of the ostrovsky equation converges to the solution of the kdv equation when the rotation parameter goes to 0 and the initial data of the kdv equation is in l2 to show this result we prove a bilinear estimate which is uniform with respect to

a theory for multiresolution signal decomposition the wavelet representation multiresolution representations are effective for analyzing the information content of images the properties of the operator which approximates a signal at a given resolution were studied it is shown that the difference of information between the approximation of a signal at the resolutions 2 sup j 1 and 2 sup j where j is an integer can be extracted by decomposing this signal on a wavelet orthonormal basis of l sup 2 r sup n the vector space of measurable square integrable n dimensional functions in l sup 2 r a wavelet orthonormal basis is a family of functions which is built by dilating and translating a unique function psi x this decomposition defines an orthogonal multiresolution representation called a wavelet representation it is computed with a pyramidal algorithm based on convolutions with quadrature mirror filters wavelet representation lies between the spatial and fourier domains for images the wavelet representation differentiates several spatial orientations the application of this representation to data compression in image coding texture discrimination and fractal analysis is discussed