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Global well-posedness of the non-isentropic full compressible magnetohydrodynamic equations
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In this paper, we are concerned with Cauchy problem for the multi-dimensional (N ≥ 3) non-isentropic full compressible magnetohydrodynamic equations. We prove the existence and uniqueness of a global strong solution to the system for the initial data close to a stable equilibrium state in critical Besov spaces. Our method is mainly based on the uniform estimates in Besov spaces for the proper linearized system with convective terms. 相似文献
3.
The global solutions in critical spaces to the multi-dimensional compressible viscoelastic flows are considered. The global existence of the Cauchy problem with initial data close to an equilibrium state is established in Besov spaces. Using uniform estimates for a hyperbolic-parabolic linear system with convection terms, we prove the global existence in the Besov space which is invariant with respect to the scaling of the associated equations. Several important estimates are achieved, including a smoothing effect on the velocity, and the L1-decay of the density and deformation gradient. 相似文献
4.
Sandrine Dubois 《Journal of Differential Equations》2003,189(1):99-147
We exhibit simple sufficient conditions which give weak-strong uniqueness for the 3D Navier-Stokes equations. The main tools are trilinear estimates and energy inequalities. We then apply our result to the framework of Lorentz, Morrey and Besov over Morrey spaces so as to get new weak-strong uniqueness classes and so uniqueness classes for solutions in the Leray-Hopf class. In the last section, we give a uniqueness and regularity result. We obtain new uniqueness classes for solutions in the Leray-Hopf class without energy inequalities but sufficiently regular. 相似文献
5.
Koch Herbert 《偏微分方程通讯》2013,38(3-4):389-437
We prove that classical C1–solutions to phase transition problems, which include the two–phase Stefan problem, are smooth. The problem is reduced to a fixed domain using von Mises variables. The estimates are obtained by frozen coefficients and new Lp estimates for linear parabolic equations with dynamic boundary condition. Crucial ingredients are the observation that a certain function is a Fourier multiplier, an approximation procedure of norms in Besov spaces and Meyer' approach to Nemytakij operators. 相似文献
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Yongqiang Ren Aijie Cheng Hong Wang 《Numerical Methods for Partial Differential Equations》2014,30(1):17-43
We prove an optimal‐order error estimate in a weighted energy norm for finite volume method for two‐dimensional time‐dependent advection–diffusion equations on a uniform space‐time partition of the domain. The generic constants in the estimates depend only on certain norms of the true solution but not on the scaling parameter. These estimates, combined with a priori stability estimates of the governing partial differential equations with full regularity, yield a uniform estimate of the finite volume method, in which the generic constants depend only on the Sobolev norms of the initial and right side data but not on the scaling parameter. We use the interpolation of spaces and stability estimates to derive a uniform estimate for problems with minimal or intermediate regularity, where the convergence rates are proportional to certain Besov norms of the initial and right‐hand side data. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 17‐43, 2014 相似文献
7.
Ryo Takada 《Journal of Evolution Equations》2008,8(4):693-725
We introduce Besov type function spaces, based on the weak L
p
-spaces instead of the standard L
p
-spaces, and prove a local-in-time unique existence and a blow-up criterion of solutions in those spaces for the Euler equations
of perfect incompressible fluid in . For the proof, we establish the Beale-Kato-Majda type logarithmic inequality and commutator type estimates in our weak spaces.
Abbreviate title: Euler equations in Besov spaces of weak type 相似文献
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This paper is devoted to the global in time existence of classical solutions to the d-Dimensional (dD) micropolar equations with fractional dissipation. Micropolar equations model a class of fluids with nonsymmetric stress tensor such as fluids consisting of particles suspended in a viscous medium. It remains unknown whether or not smooth solutions of the classical 3D micropolar equations can develop finite-time singularities. The purpose here is to explore the global regularity of solutions for dD micropolar equations under the smallest amount of dissipation. We establish the global regularity for two important fractional dissipation cases. Direct energy estimates are not sufficient to obtain the desired global a priori bounds in each case. To overcome the difficulties, we employ the Besov space techniques. 相似文献
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Jun Xiong Jia 《数学学报(英文版)》2018,34(5):855-872
In this paper, we study the optimal time decay rate of isentropic Navier–Stokes equations under the low regularity assumptions about initial data. In the previous works about optimal time decay rate, the initial data need to be small in H~([N/2]+2)(R~N). Our work combined negative Besov space estimates and the conventional energy estimates in Besov space framework which is developed by Danchin. Through our methods, we can get optimal time decay rate with initial data just small in B~(N/2-1,N/2+1)∩B~(N/2-1,N/2) and belong to some negative Besov space(need not to be small). Finally,combining the recent results in [25] with our methods, we only need the initial data to be small in homogeneous Besov spaceB~(N/2-2,N/2)∩B~(N/2-1) to get the optimal time decay rate in space L~2. 相似文献
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Anna L. Mazzucato 《Transactions of the American Mathematical Society》2003,355(4):1297-1364
This paper is devoted to the analysis of function spaces modeled on Besov spaces and their applications to non-linear partial differential equations, with emphasis on the incompressible, isotropic Navier-Stokes system and semi-linear heat equations. Specifically, we consider the class, introduced by Hideo Kozono and Masao Yamazaki, of Besov spaces based on Morrey spaces, which we call Besov-Morrey or BM spaces. We obtain equivalent representations in terms of the Weierstrass semigroup and wavelets, and various embeddings in classical spaces. We then establish pseudo-differential and para-differential estimates. Our results cover non-regular and exotic symbols. Although the heat semigroup is not strongly continuous on Morrey spaces, we show that its action defines an equivalent norm. In particular, homogeneous BM spaces belong to a larger class constructed by Grzegorz Karch to analyze scaling in parabolic equations. We compare Karch's results with those of Kozono and Yamazaki and generalize them by obtaining short-time existence and uniqueness of solutions for arbitrary data with subcritical regularity. We exploit pseudo-differential calculus to extend the analysis to compact, smooth, boundaryless, Riemannian manifolds. BM spaces are defined by means of partitions of unity and coordinate patches, and intrinsically in terms of functions of the Laplace operator.
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In this paper we consider the local and global well-posedness to the density-dependent incompressible viscoelastic fluids. We first study some linear models associated to the incompressible viscoelastic system. Then we approximate the system by a sequence of ordinary differential equations, by means of the Friedrichs method. Some uniform estimates for those solutions will be obtained. Using compactness arguments, we will get the local existence up to extracting a subsequence by means of Ascoli’s lemma. With the help of small data conditions and hybird Besov spaces, we finally derive the global existence. 相似文献
12.
《中国科学 数学(英文版)》2015,(5)
The present paper first obtains Strichartz estimates for parabolic equations with nonnegative elliptic operators of order 2m by using both the abstract Strichartz estimates of Keel-Tao and the Hardy-LittlewoodSobolev inequality. Some conclusions can be viewed as the improvements of the previously known ones. Furthermore, an endpoint homogeneous Strichartz estimates on BMOx(Rn) and a parabolic homogeneous Strichartz estimate are proved. Meanwhile, the Strichartz estimates to the Sobolev spaces and Besov spaces are generalized. Secondly, the local well-posedness and small global well-posedness of the Cauchy problem for the semilinear parabolic equations with elliptic operators of order 2m, which has a potential V(t, x) satisfying appropriate integrable conditions, are established. Finally, the local and global existence and uniqueness of regular solutions in spatial variables for the higher order elliptic Navier-Stokes system with initial data in Lr(Rn) is proved. 相似文献
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Winfried Sickel Frauke Sprengel 《Journal of Computational Analysis and Applications》1999,1(3):263-288
We investigate the order of convergence of periodic interpolation on sparse grids (blending interpolation) in the framework of tensor products of Nikol'skij–Besov spaces. To this end, we make use of the uniformity of the considered tensor norms and provide a unified approach to error estimates for the interpolation of univariate periodic functions from Nikol'skij–Besov spaces. 相似文献
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Reinhard Hochmuth 《分析论及其应用》2002,18(1):1-25
This paper studies several problems, which are potentially relevant for the construction of adaptive numerical schemes. First, biorthogonal spline wavelets on [0,1 ] are chosen as a starting point for characterizations of functions in Besov spaces B , (0,1) with 0<σ<∞ and (1+σ)-1<τ<∞. Such function spaces are known to be related to nonlinear approximation. Then so called restricted nonlinear approximation procedures with respect to Sobolev space norms are considered. Besides characterization results Jackson type estimates for various tree-type and tresholding algorithms are investigated. Finally known approximation results for geometry induced singularity functions of boundary integeral equations are combined with the characterization results for restricted nonlinear approximation to show Besov space regularity results. 相似文献
15.
本文证明了, 在临界Besov 空间中, 速度的竖直方向具有大的初始值的三维不可压缩Navier-Stokes 方程的整体解是唯一存在的. 首先, 引进合适的权函数, 用以控制方程中的非线性项; 其次, 充分利用流体的不可压缩性质, 分别估计速度的水平分量和竖直分量以及压力的水平方向梯度和竖直方向梯度; 最后, 通过适当选取权函数的系数, 得到封闭的能量估计, 从而得到方程的整体适定性. 相似文献
16.
We give a weak-strong uniqueness result for the weak solutions of the generalized Navier-Stokes equations in Besov space. 相似文献
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Zhichun Zhai 《Journal of Mathematical Analysis and Applications》2009,356(2):642-658
We obtain Strichartz estimates for the fractional heat equations by using both the abstract Strichartz estimates of Keel-Tao and the Hardy-Littlewood-Sobolev inequality. We also prove an endpoint homogeneous Strichartz estimate via replacing by BMOx(Rn) and a parabolic homogeneous Strichartz estimate. Meanwhile, we generalize the Strichartz estimates by replacing the Lebesgue spaces with either Besov spaces or Sobolev spaces. Moreover, we establish the Strichartz estimates for the fractional heat equations with a time dependent potential of an appropriate integrability. As an application, we prove the global existence and uniqueness of regular solutions in spatial variables for the generalized Navier-Stokes system with Lr(Rn) data. 相似文献
18.
Shijun Zheng 《分析论及其应用》2007,23(4):375-379
We obtain certain time decay and regularity estimates for 3D Schroedinger equation with a potential in the Kato class by using Besov spaces associated with Schroedinger operators. 相似文献
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Shijun Zheng 《分析论及其应用》2007,23(4)
We obtain certain time decay and regularity estimates for 3D Schrodinger equation with a potential in the Kato class by using Besov spaces associated with Schrodinger operators. 相似文献
20.
Ukrainian Mathematical Journal - We obtain order estimates for the M-dimensional Kolmogorov widths of the Nikol’skii–Besov classes of periodic functions of many variables with... 相似文献