带阻尼的三维Navier-Stokes方程在Besov空间中的对数改进的正则性准则

研究了带阻尼的三维Navier-Stokes方程Cauchy问题解的正则性,得到了在Besov空间中关于速度场的对数改进的正则性准则.     

速度和磁场在负指数 Besov 空间中的非齐性磁流体方程组

本文考虑带真空的非齐性磁流体方程组, 我们给出了一个关于速度和磁场在负指数 Besov 空间中的正则性准则, 其部分改进了 [Jishan FAN, Fucai LI, G. NAKAMURA, Zhong TAN, Regularity criteria for the three-dimensional magnetohydrodynamic equations. J. Differential Equations, 2014, {\bf 256}(8): 2858--2875]. 我们的方法是建立一个新型的双线性估计.     

Morrey-Campanato空间中三维 Navier—Stokes方程的正则性准则

利用能量不等式和一些临界空间中的不等式,在Morrey—Campanato空间获得了两个只涉及水平速度场的正则性准则,改进了一些已有的结果．     

带拯救的两参数Markov碰撞过程的遍历性

本文考虑了一类带拯救的两参数Markov碰撞过程.首先讨论了带拯救的两参数Markov碰撞q-矩阵发生函数的性质,通过发生函数给出了过程的正则性和唯一性判别准则,得到了过程的常返性和遍历性的充分必要条件,并给出了几个易于验证的充分条件.最后,给出了遍历情形下该过程平稳分布的发生函数,并给出了过程强遍历的判别准则.     

二维趋化N-S方程解的唯一性准则

本文研究一类二维趋化N-S方程解的唯一性问题.利用Littlewood-Paley理论和Besov空间理论以及做差法,获得这一类二维趋化N-S方程弱解唯一性的唯一性准则.     

正则参数求解的微分进化算法

研究了正则化方法中正则参数的求解问题,提出了利用微分进化算法获取正则参数.微分进化算法属于全局最优化算法,具有鲁棒性强、收敛速度快、计算精度高的优点.把正则参数的求解问题转化为非线性优化问题,通过保持在解空间不同区域中各个点的搜索,以最大的概率找到问题的全局最优解,同时还利用数值模拟将此方法与广义交叉原理、L-曲线准则、逆最优准则等进行了对比,数值模拟结果表明该方法具有一定的可行性和有效性.     

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.     

广义磁流体方程组轴对称解的正则准则

利用能量法研究广义磁流体方程组的轴对称弱解在三维空间中的正则性,得到了用方位角分量控制的正则准则,该准则表明方位角分量起主导作用.     

带移民的碰撞分枝过程的唯一性

本文提出了一种带移民的碰撞分枝过程,它由三部分组成:马氏分枝过程、碰撞分枝过程和状态独立的移民过程,给出了该过程正则性和唯一性判别准则。     

三维磁微极流体方程弱解的正则性

本文给出了磁微极流体方程弱解的一个新的正则性准则:如果u满足uz ∈Lq(0,T;Lp(R3)),其中p≥3且满足3/p+2/q≤1,那么弱解(u,ω,b)在(0,T)是光滑解.     

On the regularity of -Borel ideals

In this paper we prove Pardue's conjecture on the regularity of principal -Borel ideals. As a consequence we obtain an upper bound for the regularity of general -Borel ideals.

     

Regularity of the Solution to the Dirichlet Problem in Morrey Spaces

The aim of this paper is to study Morrey regularity of the solution to the Dirichlet problem for second order elliptic equation of the form Lu = -(a_{ij}u_x_i + b_j_u)_x_j + du = e + (f_j)x_j in a bounded open subset of Rn(n ≥ 3), where b_j , d, e, f_j are assumed to be in some Morrey spaces.     

On the regularity criteria of the 3D Navier-Stokes equations in critical spaces

Regularity criteria of Leray-Hopf weak solutions to the three-dimensional Navier-Stokes equations in some critical spaces such as Lorentz space, Morrey space and multiplier space are derived in terms of two partial derivatives, 1 u 1 , 2 u 2 , of velocity fields.     

Regularities of the solutions to the Fokker-Planck-Boltzmann equation

In this paper, we consider the regularities of the solutions to the Fokker-Planck-Boltzmann equation. In particular, we prove that for hard sphere case, the strong solution constructed by Li and Matsumura [H. Li, A. Matsumura, Behavior of the Fokker-Planck-Boltzmann equation near a Maxwellian, Arch. Ration. Mech. Anal. (2008), in press] near Maxwellian becomes immediately smooth with respect to all variables as long as t>0.     

BMO and the regularity criterion for weak solutions to the magnetohydrodynamic equations

In this paper, we study the regularity criterion for weak solutions to the incompressible magnetohydrodynamic equations. We derive the regularity of weak solutions in the marginal class. Moreover, our result demonstrates that the velocity field of the fluid plays a more dominant role than the magnetic field does on the regularity of solutions to the magnetohydrodynamic equations.     

On the regularity of generalized MHD equations

This paper studies the regularity of generalized magneto-hydrodynamics equation on the condition 0<α=β<3/2. It will show if ∇u∈Lp,q on [0,T) with