on the vanishing viscosity limit for the 3d navier stokes equations with a slip boundary condition where and below and denote the div and curl operators respectively n is the outward normal and is the unit tangential vector of the investigation of vanishing viscosity limit of solutions of the navier stokes equations both in the two and three spacial dimensional cases is a classical issue there are two related questions arising from here one is how to describe the inviscid limiting behavior of the navier stokes equation and the other is that does the euler equation can be approximated by the navier stokes equations in the case that the solution to the this research is supported in part by zheng ge ru foundation and hong kong rgc earmarked research grants cuhk 4028 04p cuhk 4040 02p and cuhk 4279 00p

on a magnetohydrodynamic problem of euler type abstract the magnetohydrodynamic or mhd equations of an incompressible and homogeneous plasma are considered in the limit of vanishing viscosity and resistivity the plasma spreading over a smoothly bounded domain g of r n n 2 the problem is posed and solved as an equation of evolution in a space of divergence free vector fields parallel to the boundary of g main results are existence uniqueness and regularity of maximal solutions and continuous dependence on forcing terms and initial data the proof of existence is based on galerkin s method and a priori estimates the continuity result is obtained by use of a regularization procedure the approach is inspired by the work of r temam and t kato and c y lai on the euler equations of ideal fluid flow

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

fusion operators in the generalized τ 2 model and root of unity symmetry of the xxz spin chain of higher spin we construct the fusion operators in the generalized 2 model using the fused l operators and verify the fusion relations with the truncation identity the algebraic bethe ansatz discussion is conducted on two special classes of 2 which include the superintegrable chiral potts model we then perform the parallel discussion on the xxz spin chain at roots of unity and demonstrate that the sl2 loop algebra symmetry exists for the root of unity xxz spin chain with a higher spin where the evaluation parameters for the symmetry algebra are identified by the explicit fabricius mccoy current for the bethe states parallels are also drawn to the comparison with the superintegrable chiral potts model

iterative shrinkage algorithm for patch smoothness regularized medical image recovery we introduce a fast iterative shrinkage algorithm for patch smoothness regularization of inverse problems in medical imaging this approach is enabled by the reformulation of current non local regularization schemes as an alternating algorithm to minimize a global criterion the proposed algorithm alternates between evaluating the denoised inter patch differences by shrinkage and computing an image that is consistent with the denoised inter patch differences and measured data we derive analytical shrinkage rules for several penalties that are relevant in non local regularization the redundancy in patch comparisons used to evaluate the shrinkage steps are exploited using convolution operations the resulting algorithm is observed to be considerably faster than current alternating non local algorithms the proposed scheme is applicable to a large class of inverse problems including deblurring denoising and fourier inversion the comparisons of the proposed scheme with state of the art regularization schemes in the context of recovering images from undersampled fourier measurements demonstrate a considerable reduction in alias artifacts and preservation of edges

a douglas rachford splitting approach to compressed sensing image recovery using low rank regularization in this paper we study the compressed sensing cs image recovery problem the traditional method divides the image into blocks and treats each block as an independent sub cs recovery task this often results in losing global structure of an image in order to improve the cs recovery result we propose a nonlocal nl estimation step after the initial cs recovery for denoising purpose the nl estimation is based on the well known nl means filtering that takes an advantage of self similarity in images we formulate the nl estimation as the low rank matrix approximation problem where the low rank matrix is formed by the nl similarity patches an efficient algorithm nonlocal douglas rachford nldr based on douglas rachford splitting is developed to solve this low rank optimization problem constrained by the cs measurements experimental results demonstrate that the proposed nldr algorithm achieves significant performance improvements over the state of the art in cs image recovery

the tq equation of the eight vertex model for complex elliptic roots of unity we extend our studies of the tq equation introduced by baxter in his 1972 solution of the eight vertex model with parameter given by 2l 2m1k im2k from m2 0 to the more general case of complex we find that there are several different cases depending on the parity of m1 and m2

generalised nonlocal image smoothing we propose a discrete variational approach for image smoothing consisting of nonlocal data and smoothness constraints that penalise general dissimilarity measures defined on image patches one of such dissimilarity measures is the weighted l 2 distance between patches in such a case we derive an iterative neighbourhood filter that induces a new similarity measure in the photometric domain it can be regarded as an extended patch similarity measure that evaluates not only the patch similarity of two chosen pixels but also the similarity of their corresponding neighbours this leads to a more robust smoothing process since the pixels selected for averaging are more coherent with the local image structure by slightly modifying the way the similarities are computed we obtain two related filters the nl means filter of buades et al siam multiscale model simul 4 2 490 530 2005b and the nds filter of mrazek et al geometric properties for incomplete data computational imaging and vision vol 31 pp 335 352 springer dordrecht 2006 in fact the proposed approach can be considered as a generalisation of the latter filter to the space of patches we also provide novel insights into relations of the nds filter with diffusion regularisation methods as well as with some recently proposed graph regularisation techniques we evaluate our method for the task of denoising greyscale and colour images degraded with gaussian and salt and pepper noise demonstrating that it compares very well to other more sophisticated approaches

a fast adaptive parameter estimation for total variation image restoration estimation of the regularization parameter which strikes a balance between the data fidelity and regularity is essential for successfully solving ill posed image restoration problems based on the classical total variation tv model and prevalent alternating direction method of multipliers we hammer out a fast algorithm being able to simultaneously estimate the regularization parameter and restore the degraded image by applying variable splitting technique to both the regularization term and data fidelity term we overcome the nondifferentiability of tv and achieve a closed form to update the regularization parameter in each iteration the solution is guaranteed to satisfy morozov s discrepancy principle furthermore we present a convergence proof for the proposed algorithm on the premise of a variable regularization parameter experimental results demonstrate that the proposed algorithm is superior in speed and competitive in accuracy compared with several state of the art methods besides the proposed method can be smoothly extended to the multichannel image restoration

abstract cauchy problem for weakly continuous operators abstract we discuss the solvability of the abstract cauchy problem u t a u t for t 0 and u 0 u 0 d where d is a weakly closed subset of a banach space y continuously embedded in the underlying banach space x and a is a nonlinear operator from d into x satisfying a local weak continuity condition described by a family of functionals we introduce a new type of weak compactness on the level sets of functionals and give a necessary and sufficient condition for the existence of a weakly continuously differentiable solution satisfying a growth condition we apply the abstract result obtained to the cauchy problem for a nonlinear schrodinger equation and a mixed problem for a logarithmic wave equation

stability well posedness and blow up criterion for the incompressible slice model abstract in atmospheric science slice models are frequently used to study the behaviour of weather and specifically the formation of atmospheric fronts whose prediction is fundamental in meteorology in 2013 cotter and holm introduced a new slice model which they formulated using hamilton s variational principle modified for this purpose in this paper we show the local existence and uniqueness of strong solutions of the related ism incompressible slice model the ism is a modified version of the cotter holm slice model chsm that we have obtained by adapting the lagrangian function in hamilton s principle for chsm to the euler boussinesq eady incompressible case besides proving local existence and uniqueness in this paper we also construct a blow up criterion for the ism and study arnold s stability around a restricted class of equilibrium solutions these results establish the potential applicability of the ism equations in physically meaningful situations

a nonlocal tv based variational method for polsar data speckle reduction in this paper we propose a nonlocal total variation nltv based variational model for polarimetric synthetic aperture radar polsar data speckle reduction this model named wisnltv is obtained based on the wishart fidelity term and the nltv regularization defined for the complex valued fourth order tensor data since the proposed model is non convex an equivalent bi convex model is obtained using the property of conjugate functions then an efficient iteration algorithm is developed to solve the equivalent bi convex model based on the alternating minimization and the forward backward operator splitting technique the proposed iteration algorithm is proved to be convergent under certain conditions theoretically and numerically experimental results on both synthetic and real polsar data demonstrate that the proposed method can effectively reduce speckle noise and meanwhile better preserve the details and the repetitive structures such as textures and edges and the polarimetric scattering characteristics compared with the other methods

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

strongly stratified limit for the 3d inviscid boussinesq equations we consider the initial value problem of the 3d inviscid boussinesq equations for stably stratified fluids we prove the long time existence of classical solutions for large initial data when the buoyancy frequency is sufficiently high furthermore we consider the singular limit of the strong stratification and show that the long time classical solution converges to that of 2d incompressible euler equations in some space time strichartz norms

on the blow up of solutions of the 3 d euler equations in a bounded domain it is shown that if 0 hat t is the maximal interval of existence of a smooth solutionu of the incompressible euler equations in a bounded simply connected domain subseteq r3 then int 0 hat t left omega cdot t right l infty omega dt infty where u is the vorticity crucial to this result is a special estimate proven in of the maximum velocity gradient in terms of the maximum vorticity and a logarithmic term involving a higher norm of the vorticity

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

a majorize minimize framework for rician and non central chi mr images the statistics of many mr magnitude images are described by the non central chi ncc family of probability distributions which includes the rician distribution as a special case these distributions have complicated negative log likelihoods that are nontrivial to optimize this paper describes a novel majorize minimize framework for ncc data that allows penalized maximum likelihood estimates to be obtained by solving a series of much simpler regularized least squares surrogate problems the proposed framework is general and can be useful in a range of applications we illustrate the potential advantages of the framework with real and simulated data in two contexts 1 mr image denoising and 2 diffusion profile estimation in high angular resolution diffusion mri the proposed approach is shown to yield improved results compared to methods that model the noise statistics inaccurately and faster computation relative to commonly used nonlinear optimization techniques

vanishing viscosity limit for a coupled navier stokes allen cahn system abstract in this paper we study the vanishing viscosity limit for a coupled navier stokes allen cahn system in a bounded domain we first show the local existence of smooth solutions of the euler allen cahn equations by modified galerkin method then using the boundary layer function to deal with the mismatch of the boundary conditions between navier stokes and euler equations and assuming that the energy dissipation for navier stokes equation in the boundary layer goes to zero as the viscosity tends to zero we prove that the solutions of the navier stokes allen cahn system converge to that of the euler allen cahn system in a proper small time interval in addition for strong solutions of the navier stokes allen cahn system in 2d the convergence rate is c 1 2

nonlocal regularization of inverse problems a unified variational framework we introduce a unifying energy minimization framework for nonlocal regularization of inverse problems in contrast to the weighted sum of square differences between image pixels used by current schemes the proposed functional is an unweighted sum of inter patch distances we use robust distance metrics that promote the averaging of similar patches while discouraging the averaging of dissimilar patches we show that the first iteration of a majorize minimize algorithm to minimize the proposed cost function is similar to current nonlocal methods the reformulation thus provides a theoretical justification for the heuristic approach of iterating nonlocal schemes which re estimate the weights from the current image estimate thanks to the reformulation we now understand that the widely reported alias amplification associated with iterative nonlocal methods are caused by the convergence to local minimum of the nonconvex penalty we introduce an efficient continuation strategy to overcome this problem the similarity of the proposed criterion to widely used nonquadratic penalties e g total variation and lp semi norms opens the door to the adaptation of fast algorithms developed in the context of compressive sensing we introduce several novel algorithms to solve the proposed nonlocal optimization problem thanks to the unifying framework these fast algorithms are readily applicable for a large class of distance metrics

non regular eigenstate of the xxx model as some limit of the bethe state for the one dimensional xxx model under the periodic boundary conditions we discuss two types of eigenvectors regular eigenvectors which have finite valued rapidities satisfying the bethe ansatz equations and non regular eigenvectors which are descendants of some regular eigenvectors under the action of the su 2 spin lowering operator it has been pointed out by many authors that the non regular eigenvectors should correspond to the bethe ansatz wavefunctions which have multiple infinite rapidities however it has not been explicitly shown whether such a delicate limiting procedure is possible in this paper we discuss it explicitly at the level of wavefunctions we prove that any non regular eigenvector of the xxx model is derived from the bethe ansatz wavefunctions through some limit of infinite rapidities we formulate the regularization also in terms of the algebraic bethe ansatz method as an application of infinite rapidity we discuss the period of the spectral flow under the twisted periodic boundary conditions

vanishing viscosity limit for the 3d magnetohydrodynamic system with a slip boundary condition abstract this work investigates the solvability regularity and vanishing viscosity limit of the 3d viscous magnetohydrodynamic system in a class of bounded domains with a slip boundary condition

limiting case of the sobolev inequality in bmo with application to the euler equations we shall prove a logarithmic sobolev inequality by means of the bmo norm in the critical exponents as an application we shall establish a blow up criterion of solutions to the euler equations

regular xxz bethe states at roots of unity as highest weight vectors of the sl2 loop algebra we show that every regular bethe ansatz eigenvector of the xxz spin chain at roots of unity is a highest weight vector of the sl2 loop algebra for some restricted sectors with respect to eigenvalues of the total spin operator sz and evaluate explicitly the highest weight in terms of the bethe roots we also discuss whether a given regular bethe state in the sectors generates an irreducible representation or not in fact we present such a regular bethe state in the inhomogeneous case that generates a reducible weyl module here we call a solution of the bethe ansatz equations which is given by a set of distinct and finite rapidities regular bethe roots we call a nonzero bethe ansatz eigenvector with regular bethe roots a regular bethe state

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

viscous boundary layers for the navier stokes equations with the navier slip conditions we tackle the issue of the inviscid limit of the incompressible navier stokes equations when the navier slip with friction conditions are prescribed on impermeable boundaries we justify an asymptotic expansion which involves a weak amplitude boundary layer with the same thickness as in prandtl s theory and a linear behavior this analysis holds for general regular domains in both dimensions two and three

smooth solutions for motion of a rigid body of general form in an incompressible perfect fluid in this paper we consider the interactions between a rigid body of general form and the incompressible perfect fluid surrounding it local well posedness in the space c 0 t hs is obtained for the fluid rigid body system

bethe s equation is incomplete for the xxz model at roots of unity we demonstrate for the six vertex and xxz model parameterized by q q 1 2 1 that when q2n 1 for integer n 2 the bethe s ansatz equations determine only the eigenvectors which are the highest weights of the infinite dimensional sl2 loop algebra symmetry group of the model therefore in this case the bethe s ansatz equations are incomplete and further conditions need to be imposed in order to completely specify the wave function we discuss how the evaluation parameters of the finite dimensional representations of the sl2 loop algebra can be used to complete this specification

a new boundary condition for the three dimensional navier stokes equation and the vanishing viscosity limit in this paper we propose a new vorticity boundary condition for the three dimensional incompressible navier stokes equation for a general smooth domain in r3 this boundary condition is motivated by the generalized navier slip boundary condition involving the vorticity it is shown first that such an initial boundary value problem is well posed at least local in time furthermore more importantly we obtain some estimates on rate of convergence in c 0 t h1 and c 0 t h2 of the solutions to the corresponding solutions of the ideal euler equations with the standard slip boundary condition

the q operator and functional relations of the eight vertex model at root of unity for odd n following baxter s method of producing q 72 operator we construct the q operator of the root of unity eight vertex model for the crossing parameter 2mk n with odd n where q 72 does not exist we use this new q operator to study the functional relations in the fabricius mccoy comparison between the root of unity eight vertex model and the superintegrable n state chiral potts model by the compatibility of the constructed q operator with the structure of baxter s eight vertex solid on solid sos model we verify the set of functional relations of the root of unity eight vertex model using the explicit form of the q operator and fusion weights of the sos model

the initial value problem for elastodynamics of incompressible bodies we prove short time well posedness of the cauchy problem for incompressible strongly elliptic hyperelastic materials

deterministic edge preserving regularization in computed imaging many image processing problems are ill posed and must be regularized usually a roughness penalty is imposed on the solution the difficulty is to avoid the smoothing of edges which are very important attributes of the image in this paper we first give conditions for the design of such an edge preserving regularization under these conditions we show that it is possible to introduce an auxiliary variable whose role is twofold first it marks the discontinuities and ensures their preservation from smoothing second it makes the criterion half quadratic the optimization is then easier we propose a deterministic strategy based on alternate minimizations on the image and the auxiliary variable this leads to the definition of an original reconstruction algorithm called artur some theoretical properties of artur are discussed experimental results illustrate the behavior of the algorithm these results are shown in the field of 2d single photon emission tomography but this method can be applied in a large number of applications in image processing

completing bethe s equations at roots of unity in a previous paper we demonstrated that bethe s equations are not sufficient to specify the eigenvectors of the xxz model at roots of unity for states where the hamiltonian has degenerate eigenvalues we here find the equations which will complete the specification of the eigenvectors in these degenerate cases and present evidence that the sl 2 loop algebra symmetry is sufficiently powerful to determine that the highest weight of each irreducible representation is given by bethe s ansatz

a fast multilevel algorithm for wavelet regularized image restoration we present a multilevel extension of the popular ldquothresholded landweberrdquo algorithm for wavelet regularized image restoration that yields an order of magnitude speed improvement over the standard fixed scale implementation the method is generic and targeted towards large scale linear inverse problems such as 3 d deconvolution microscopy the algorithm is derived within the framework of bound optimization the key idea is to successively update the coefficients in the various wavelet channels using fixed subband adapted iteration parameters step sizes and threshold levels the optimization problem is solved efficiently via a proper chaining of basic iteration modules the higher level description of the algorithm is similar to that of a multigrid solver for pdes but there is one fundamental difference the latter iterates though a sequence of multiresolution versions of the original problem while in our case we cycle through the wavelet subspaces corresponding to the difference between successive approximations this strategy is motivated by the special structure of the problem and the preconditioning properties of the wavelet representation we establish that the solution of the restoration problem corresponds to a fixed point of our multilevel optimizer we also provide experimental evidence that the improvement in convergence rate is essentially determined by the unconstrained linear part of the algorithm irrespective of the type of wavelet finally we illustrate the technique with some image deconvolution examples including some real 3 d fluorescence microscopy data

properties of the string operator in the eight vertex model the construction of creation operators of exact strings in eigenvectors of the eight vertex model at elliptic roots of unity of the crossing parameter which allow the generation of the complete set of degenerate eigenstates is based on the conjecture that the naive string operator vanishes in this paper we present a proof of this conjecture furthermore we show that for chains of odd length the string operator is either proportional to the symmetry operator s or vanishes depending on the precise form of the crossing parameter

vanishing viscosity limit for incompressible navier stokes equations with navier boundary conditions for small slip length in this paper we will analyze the vanishing viscosity limit of the incompressible navier stokes equations with the navier slip boundary conditions in a bounded domain of r2 when the slip length is smaller than or equal to the order of viscosity by using an energy method and developing kato s approach given in the work of kato math sci res inst publ 2 85 98 1984 we obtain several conditions to guarantee that the solution of the navier stokes equations with the navier slip boundary conditions goes to the solution of the associated problem of the euler equations in the energy space l2 uniformly in time as the viscosity goes to zero

construction of some missing eigenvectors of the xyz spin chain at the discrete coupling constants and the exponentially large spectral degeneracy of the transfer matrix we discuss an algebraic method for constructing eigenvectors of the transfer matrix of the eight vertex model at the discrete coupling parameters we consider the algebraic bethe ansatz of the elliptic quantum group e sl2 for the case where the parameter satisfies 2n m1 m2 for arbitrary integers n m1 and m2 when m1 or m2 is odd the eigenvectors thus obtained have not been discussed previously furthermore we construct a family of degenerate eigenvectors of the xyz spin chain some of which are shown to be related to the sl2 loop algebra symmetry of the xxz spin chain we show that the dimension of some degenerate eigenspace of the xyz spin chain on l sites is given by n2l n if l n is an even integer the construction of eigenvectors of the transfer matrices of some related interaction round a face models is also discussed

on approximate solutions of the equations of incompressible magnetohydrodynamics abstract inspired by an approach proposed previously for the incompressible navier stokes ns equations we present a general framework for the a posteriori analysis of the equations of incompressible magnetohydrodynamics mhd on a torus of arbitrary dimension d this setting involves a sobolev space of infinite order made of c vector fields with vanishing divergence and mean on the torus given any approximate solution of the mhd cauchy problem its a posteriori analysis with the method of the present work allows one to infer a lower bound on the time of existence of the exact solution and to bound from above the sobolev distance of any order between the exact and the approximate solution in certain cases the above mentioned lower bound on the time of existence is found to be infinite so one infers the global existence of the exact mhd solution we present some applications of this general scheme the most sophisticated one lives in dimension d 3 with the abc flow perturbed magnetically as an initial datum and uses for the cauchy problem a galerkin approximate solution in 124 fourier modes we illustrate the conclusions arising in this case from the a posteriori analysis of the galerkin approximant these include the derivation of global existence of the exact mhd solution with the abc datum when the dimensionless viscosity and resistivity are equal and stay above a critical value

dissipative solutions and semiflow selection for the complete euler system to circumvent the ill posedness issues present in various models of continuum fluid mechanics we present a dynamical systems approach aiming at the selection of physically relevant solutions even under the presence of infinitely many solutions to the full euler system describing the motion of a compressible inviscid fluid our approach permits to select a system of solutions one trajectory for every initial condition satisfying the classical semiflow property moreover the selection respects the well accepted admissibility criteria for physical solutions namely maximization of the entropy production rate and the weak strong uniqueness principle consequently strong solutions are always selected whenever they exist and stationary states are stable and included in the selection as well to this end we introduce a notion of dissipative solution which is given by a triple of density momentum and total entropy defined as expectations of a suitable measure valued solution

majorization minimization algorithms for wavelet based image restoration standard formulations of image signal deconvolution under wavelet based priors regularizers lead to very high dimensional optimization problems involving the following difficulties the non gaussian heavy tailed wavelet priors lead to objective functions which are nonquadratic usually nondifferentiable and sometimes even nonconvex the presence of the convolution operator destroys the separability which underlies the simplicity of wavelet based denoising this paper presents a unified view of several recently proposed algorithms for handling this class of optimization problems placing them in a common majorization minimization mm framework one of the classes of algorithms considered when using quadratic bounds on nondifferentiable log priors shares the infamous singularity issue si of iteratively re weighted least squares irls algorithms the possibility of having to handle infinite weights which may cause both numerical and convergence issues in this paper we prove several new results which strongly support the claim that the si does not compromise the usefulness of this class of algorithms exploiting the unified mm perspective we introduce a new algorithm resulting from using bounds for nonconvex regularizers the experiments confirm the superior performance of this method when compared to the one based on quadratic majorization finally an experimental comparison of the several algorithms reveals their relative merits for different standard types of scenarios

derivative estimates for the navier stokes equations in a three dimensional region on etablit des estimations fractionnaires pour les solutions de l equation de navier stokes dans le cas d un domaine avec une limite sur laquelle les composantes des solutions s annulent la condition de limite fixee appropriee pour des ecoulements visqueux

higher order commutator estimates and local existence for the non resistive mhd equations and related models this paper establishes the local in time existence and uniqueness of strong solutions in hs for s n 2 to the viscous non resistive magnetohydrodynamics mhd equations in rn n 2 3 as well as for a related model where the advection terms are removed from the velocity equation the uniform bounds required for proving existence are established by means of a new estimate which is a partial generalisation of the commutator estimate of kato ponce comm pure appl math 41 7 891 907 1988

almost sure existence of global weak solutions for incompressible mhd equations in negative order sobolev space abstract in this paper we consider the cauchy problem of the incompressible magnetohydrodynamics mhd equations in the periodic space domain t n where n 2 after a suitable randomization to the initial data we obtain the almost sure existence of global weak solutions with the initial data in h s t n s 1 0 specially the global weak solution is unique when n 2

a priori estimates for free boundary problem of incompressible inviscid magnetohydrodynamic flows in the present paper we prove the a priori estimates of sobolev norms for a free boundary problem of the incompressible inviscid magnetohydrodynamics equations in all physical spatial dimensions n 2 and 3 by adopting a geometrical point of view used in christodoulou and lindblad commun pure appl math 53 1536 1602 2000 and estimating quantities such as the second fundamental form and the velocity of the free surface we identify the well posedness condition thattheouternormalderivativeofthetotalpressureincludingthefluidandmagnetic pressuresisnegativeonthefreeboundary whichissimilartothephysicalcondition taylor sign condition for the incompressible euler equations of fluids

on representations of the elliptic quantum group e τ η sl 2 we describe representation theory of the elliptic quantum groupe sl 2 it turns out that the representation theory is parallel to the representation theory of the yangiany sl 2 and the quantum loop group u q widetilde sl 2 we introduce basic notions of representation theory of the elliptic quantum groupe sl 2 and construct three families of modules evaluation modules cyclic modules one dimensional modules we show that under certain conditions any irreducible highest weight module of finite type is isomorphic to a tensor product of evaluation modules and a one dimensional module we describe fusion of finite dimensional evaluation modules in particular we show that under certain conditions the tensor product of two evaluation modules becomes reducible and contains an evaluation module in this case the imbedding of the evaluation module into the tensor product is given in terms of elliptic binomial coefficients we describe the determinant element of the elliptic quantum group representation theory becomes special ifn m l wheren m l are integers we indicate some new features in this case

smooth solutions for the motion of a ball in an incompressible perfect fluid in this paper we investigate the motion of a rigid ball surrounded by an incompressible perfect fluid occupying rn we prove the existence uniqueness and persistence of the regularity for the solutions of this fluid structure interaction problem

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

motion adaptive patch based low rank approach for compressed sensing cardiac cine mri one of the technical challenges in cine magnetic resonance imaging mri is to reduce the acquisition time to enable the high spatio temporal resolution imaging of a cardiac volume within a short scan time recently compressed sensing approaches have been investigated extensively for highly accelerated cine mri by exploiting transform domain sparsity using linear transforms such as wavelets and fourier however in cardiac cine imaging the cardiac volume changes significantly between frames and there often exist abrupt pixel value changes along time in order to effectively sparsify such temporal variations it is necessary to exploit temporal redundancy along motion trajectories this paper introduces a novel patch based reconstruction method to exploit geometric similarities in the spatio temporal domain in particular we use a low rank constraint for similar patches along motion based on the observation that rank structures are relatively less sensitive to global intensity changes but make it easier to capture moving edges a nash equilibrium formulation with relaxation is employed to guarantee convergence experimental results show that the proposed algorithm clearly reconstructs important anatomical structures in cardiac cine image and provides improved image quality compared to existing state of the art methods such as k t focuss k t slr and master

convergence of the 2d euler α to euler equations in the dirichlet case indifference to boundary layers abstract in this article we consider the euler system as a regularization of the incompressible euler equations in a smooth two dimensional bounded domain for the limiting euler system we consider the usual non penetration boundary condition while for the euler regularization we use velocity vanishing at the boundary we also assume that the initial velocities for the euler system approximate in a suitable sense as the regularization parameter 0 the initial velocity for the limiting euler system for small values of this situation leads to a boundary layer which is the main concern of this work our main result is that under appropriate regularity assumptions and despite the presence of this boundary layer the solutions of the euler system converge as 0 to the corresponding solution of the euler equations in l 2 in space uniformly in time we also present an example involving parallel flows in order to illustrate the indifference to the boundary layer of the 0 limit which underlies our work

alternating direction method of multiplier for tomography with nonlocal regularizers the ordered subset expectation maximization osem algorithm approximates the gradient of a likelihood function using a subset of projections instead of using all projections so that fast image reconstruction is possible for emission and transmission tomography such as spect pet and ct however osem does not significantly accelerate reconstruction with computationally expensive regularizers such as patch based nonlocal nl regularizers because the regularizer gradient is evaluated for every subset we propose to use variable splitting to separate the likelihood term and the regularizer term for penalized emission tomographic image reconstruction problem and to optimize it using the alternating direction method of multiplier admm we also propose a fast algorithm to optimize the admm parameter based on convergence rate analysis this new scheme enables more sub iterations related to the likelihood term we evaluated our admm for 3 d spect image reconstruction with a patch based nl regularizer that uses the fair potential function our proposed admm improved the speed of convergence substantially compared to other existing methods such as gradient descent em and osem using de pierro s approach and the limited memory broyden fletcher goldfarb shanno algorithm

completeness of the bethe ansatz for the six and eight vertex models we discuss some of the difficulties that have been mentioned in the literature in connection with the bethe ansatz for the six vertex model and xxz chain and for the eight vertex model in particular we discuss the beyond the equator infinite momenta and exact complete string problems we show how they can be overcome and conclude that the coordinate bethe ansatz does indeed give a complete set of states as expected

new developments in the eight vertex model we demonstrate that the q matrix introduced in baxter s 1972 solution of the eight vertex model has some eigenvectors which are not eigenvectors of the spin reflection operator and conjecture a new functional equation for q v which both contains the bethe equation that gives the eigenvalues of the transfer matrix and computes the degeneracies of these eigenvalues

derivation of a bogomol ny inequality in five dimensional kaluza klein theory we prove an inequality bounding the mass from below by the electromagnetic charge in five dimensional kaluza klein theory without assuming the existence of globalu 1 symmetry

efficient nonlocal means for denoising of textural patterns this paper contributes two novel techniques in the context of image restoration by nonlocal filtering first we introduce an efficient implementation of the nonlocal means filter based on arranging the data in a cluster tree the structuring of data allows for a fast and accurate preselection of similar patches in contrast to previous approaches the preselection is based on the same distance measure as used by the filter itself it allows for large speedups especially when the search for similar patches covers the whole image domain i e when the filter is truly nonlocal however also in the windowed version of the filter the cluster tree approach compares favorably to previous techniques in respect of quality versus computational cost second we suggest an iterative version of the filter that is derived from a variational principle and is designed to yield nontrivial steady states it reveals to be particularly useful in order to restore regular textured patterns

global strong solution to the three dimensional density dependent incompressible magnetohydrodynamic flows abstract an initial boundary value problem is considered for the density dependent incompressible viscous magnetohydrodynamic flow in a three dimensional bounded domain the homogeneous dirichlet boundary condition is prescribed on the velocity and the perfectly conducting wall condition is prescribed on the magnetic field for the initial density away from vacuum the existence and uniqueness are established for the local strong solution with large initial data as well as for the global strong solution with small initial data furthermore the weak strong uniqueness of solutions is also proved which shows that the weak solution is equal to the strong solution with certain initial data

local ill posedness of the incompressible euler equations in c 1 and b 1_ infty 1 we show that the 2d euler equations are not locally well posed in the sense of hadamard in the c 1 space and in the besov space b 1 infty 1 our approach relies on the technique of lagrangian deformations of bourgain and li strong ill posedness of the incompressible euler equations in borderline sobolev spaces arxiv 1307 7090 we show that the assumption that the data to solution map is continuous in either c 1 or b 1 infty 1 leads to a contradiction with a result in w 1 p of kato and ponce rev mat iberoam 2 73 88 1986