Logarithmically improved regularity criterion for the 3D generalized magneto-hydrodynamic equations

This article proves the logarithmically improved Serrin's criterion for solutions of the 3D generalized magneto-hydrodynamic equations in terms of the gradient of the velocity field, which can be regarded as improvement of results in [10] (Luo Y W. On the regularity of generalized MHD equations. J Math Anal Appl, 2010, 365: 806–808) and [18] (Zhang Z J. Remarks on the regularity criteria for generalized MHD equations. J Math Anal Appl, 2011, 375: 799–802).     

磁场微极流方程组弱解的正则性准则

本文研究了三维空间中磁场微极流方程组弱解的正则性准则问题.利用能量估计的方法证明了如果速度场以及磁场满足一定的条件,则弱解在(0,T]是唯一的强解.     

三维Boussinesq方程的正则性准则(英文)

本文研究了三维Boussinesq方程弱解的正则性.利用精细的能量估计方法,得到了关于弱解正则性的一些充分条件,同时这些结果表明速度场比温度函数对于解的正则性起着更重要的作用.     

GLOBAL REGULARITY FOR MODIFIED CRITICAL DISSIPATIVE QUASI-GEOSTROPHIC EQUATIONS

We consider the n-dimensional modified quasi-geostrophic(SQG) equations δ_tθ + u·▽θ+kΛαθ=0, u = Λα-1R⊥θ with κ 0, α∈(0, 1] and θ0∈ W1,∞(Rn). In this paper, we establish a different proof for the global regularity of this system. The original proof was given by Constantin, Iyer, and Wu[5], who employed the approach of Besov space techniques to study the global existence and regularity of strong solutions to modified critical SQG equations for two dimensional case.The proof provided in this paper is based on the nonlinear maximum principle as well as the approach in Constantin and Vicol [2].     

一类Fuchs型方程的椭圆正则性定理

本文研究了一类锥Sobolev空间上的Fuchs型方程的解的性态,利用Bony的仿微分算子理论的方法,运用仿积、仿复合、仿线性化等工具,并结合Mellin象征的性质,得到了此类方程的椭圆正则性定理.推广了在经典Sobolev空间中的椭圆正则性结果.     

The regularity criterion of the weak solution to the 3D viscous Boussinesq equations in Besov spaces

In this paper, by using the Fourier localization technique and Bony's paraproduct decomposition, we give a regularity criterion of the weak solution to 3D viscous Boussinesq equations in Besov spaces. Copyright © 2010 John Wiley & Sons, Ltd.     

MULTIGRID METHODS FOR THE GENERALIZED STOKES EQUATIONS BASED ON MIXED FINITE ELEMENT METHODS

1. IntroductionIn this paper, we consider the fOllowing generalized stationary Stokes equations:where fl is a bounded convex domain in R', u represents the velocity of fluid, p its pressure; Fand G are external fOrce and source terms. Note that the source…     

MATHEMATICAL RESULTS RELATED TO A TWO-DIMENSIONAL MAGNETO- HYDRODYNAMIC EQUATIONS

The two-dimensional magneto-hydrodynamic (MHD) equations are considered in this article. Viscous approximations are used to obtain the local existence and uniqueness of the classical solution. When the viscous term vanishes, the convergence rates, a main problem in turbulence,are also discussed. Moreover, a blow-up criterion for our classical solution is established in terms of the magnetic fields.     

一维广义Ginzburg-Landau方程解的正则性及线性与非线性Galerkin近似

本文得到了一维广义Ginzburs－Landau方程解的Gevrey类正则性和关于时间的解析性．在此基础上得到线性Galerkin近似和非线性Galerkin近似的收敛性．     

广义Nekrasov矩阵的细分迭代判别法

利用细分矩阵下标集合的思想,构造递进系数和特殊的正对角矩阵,结合不等式的放缩,给出广义Nekrasov矩阵的迭代判别法,推广和改进了已有相关结果,并用数值实例说明了所得结果的优越性.     

A REMARK ON THE BLOW-UP CRITERION OF STRONG SOLUTIONS AND REGULARITY FOR WEAK SOLUTIONS OF NAVIER-STOKES EQUATIONS

We give blow-up criteria of strong solutions of Navier-Stokes equations with its initial data in Besov spaces and consider the regularity of Leray-Hopf solutions of the equation.     

REGULARITY OF WEAK SOLUTIONS TO MAGNETO-MICROPOLAR FLUID EQUATIONS

In this article,we study the regularity of weak solutions and the blow-up criteria for smooth solutions to the magneto-micropolar fluid equations in R~3.We obtain the classical blow-up criteria for smooth solutions(u,ω,b),i.e.,u ∈ L q(0,T;L p(R 3)) for 2 q + 3 p ≤ 1 with 3p≤∞,u ∈ C([0,T);L 3(R 3)) or u ∈L q(0,T;L p) for 3 2p≤∞ satisfying 2 q + 3p≤2.Moreover,our results indicate that the regularity of weak solutions is dominated by the velocity u of the fluid.In the end-point case p = ∞,the blow-up criteria can be extended to more general spaces u∈ L~1(0,T;B_(∞,∞)~0(R~3)).     

GEVREY CLASS REGULARITY AND APPROXIMATE INERTIAL MANIFOLDS FOR THE NEWTON-BOUSSINESQ EQUATIONS

§１．ＩｎｔｒｏｄｕｃｔｉｏｎＡｐｐｒｏｘｉｍａｔｅｉｎｅｒｔｉａｌｍａｎｉｆｏｌｄｓａｒｅｒｅｌａｔｅｄｔｏｔｈｅｓｔｕｄｙｏｆｌｏｎｇｔｉｍｅｂｅｈａｖｉｏｕｒｏｆｓｏｌｕｔｉｏｎｓｏｆｄｉｓｉｐａｔｉｖｅｐａｒｔｉａｌｄｉｆｅｒｅｎｔｉａｌｅｑ...     

一类广义Zakharov方程的精确行波解

本文研究了一类广义Zakharov方程的精确解行波解的问题.利用改进的G/G展开方法,借助于计算机代数系统Mathematica,获得了具有重要物理背景的广义Zakharov方程一系列新的含有多个参数的精确行波解,这些解包括孤立波解,双曲函数解,三角函数解,以及有理函数解.     

ON EXISTENCE， UNIQUENESS AND REGULARITY OF STEADY STATE SOLUTIONS TO THE BASIC SEMICONDUCTOR EQUATIONS

ＯＮＥＸＩＳＴＥＮＣＥ，ＵＮＩＱＵＥＮＥＳＳＡＮＤＲＥＧＵＬＡＲＩＴＹＯＦＳＴＥＡＤＹＳＴＡＴＥＳＯＬＵＴＩＯＮＳＴＯＴＨＥＢＡＳＩＣＳＥＭＩＣＯＮＤＵＣＴＯＲＥＱＵＡＴＩＯＮＳＷａｎｇＹｕａｎｍｉｎｇ（王元明）ＦａｎＪｉｓｈａｎ（樊继山）（Ｄｅｐｔ...     

A regularity criterion for the density‐dependent magnetohydrodynamic equations

In this paper, regularity criterion for the 3‐D density‐dependent magnetohydrodynamic equation is considered. It is proved that the solution keeps smoothness only under an integrable condition on the velocity field in multiplier spaces. Hence, it turns out that the velocity field plays a dominant role in the regularity criteria of the weak solutions to this nonlinear coupling problem even with density. Copyright © 2009 John Wiley & Sons, Ltd.     

REGULARITY RESULTS FOR LINEAR ELLIPTIC PROBLEMS RELATED TO THE PRIMITIVE EQUATIONS

roductlonWe establish reglllaxlty results for the GFD－Stokes system and some second order ellipticp     

一类修正的Navier—Stokes方程组Neumann边值问题的弱解

讨论一类修正的Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ型方程组Ｎｅｕｍａｎｎ边值问题的可解性及解的性质。     

Serrin-type blow-up criteria for 3D Boussinesq equations

In this article, we consider the three-dimensional Boussinesq equations with the incompressibility condition. We obtain some Serrin-type regularity conditions for the three-dimensional Boussinesq equations.