Ladyzhenskaya流体力学方程组的确定模与确定结点个数估计

论文给出了二维有界区域上Ladyzhenskaya流体力学方程组的确定模与确定结点的个数估计.结果表明若该方程组的任意两个弱解的前有限个傅立叶模有相同的渐近行为,则这两个解就具有相同的渐近行为;若该方程组的任意两个强解在有限个空间中的点上有相同的渐近行为,则这两个解几乎在整个空间上具有相同的渐近行为.     

Random attractor for a two-dimensional incompressible non-Newtonian fluid with multiplicative noise

This article proves that the random dynamical system generated by a twodimensional incompressible non-Newtonian fluid with multiplicative noise has a global random attractor, which is a random compact set absorbing any bounded nonrandom subset of the phase space.     

Uniform attractor for nonautonomous incompressible non-Newtonian fluid with a new class of external forces

This paper is joint with [27]. The authors prove in this article the existence and reveal its structure of uniform attractor for a two-dimensional nonautonomous incompressible non-Newtonian fluid with a new class of external forces.     

一类非牛顿系统弱解的长时间性态

本文讨论一类非牛顿系统弱解的长时间性态,证明解在L2 范数下的衰减速率为(1 t)-n/4 达到和线性热方程一致.     

格点系统存在指数吸引子的充分条件及应用

本文给出了一般格点动力系统存在指数吸引子的充分条件,然后将得到的结果应用到下面的格点非线性Schr(o|¨)dinger方程:iu_m-γ(2u_m-u_(m+1)-u_(m-1))+iκu_m+δ|u_m|~(2σ)u_m=g_m,m∈Z.设γ,κ,δ,σ和g_m满足适当的条件,证明了该格点方程存在指数吸引子.     

脉冲离散非线性Schr?dinger-Boussinesq方程组的统计解与分段Liouville型定理

本文研究脉冲离散非线性Schr?dinger-Boussinesq方程组的初值问题及其统计解的存在性.作者首先证明该脉冲问题的的整体适定性,然后证明解算子生成的过程存在拉回吸引子和一族不变Borel概率测度,接着给出该脉冲问题统计解的定义并证明其存在性.结果表明,该脉冲问题的统计解只关于时间分段地满足Liouville型定理.     

非自治耗散Schr\"odinger-Boussinesq 方程组紧致核截面的存在性$^$

讨论满足齐次Dirichlet边界条件的非自治耗散Schr\"odinger-Boussinesq 方程组解的长时间行为. 通过 对方程作适当的分解, 证明了方程组所生成的过程存在紧致核截面.     

一个四阶方程组在全直线上的整体吸引子

This paper studies the long time behavior of the following Cauchy problem The authors prove the existence of global attractor by showing the corresponding operator semigroup is asymptotically compact.     

EXISTENCE AND UNIQUENESS OF WEAK SOLUTIONS FOR TWO-DIMENSIONAL MODIFIED NAVIER-STOKES EQUATIONS

This paper studies a two-dimensional modified Navier-stokes equations. The author shows the existence and uniqueness of weak solutions for this equation by Galerkin method in bounded domains. The result is further extended to the case of unbounded channel-like domains.