ATTRACTORS FOR DISCRETIZATION OF GINZBURG-LANDAU-BBM EQUATIONS

Focuses on a study which discreted Ginzburg-Landau-BBM equations with periodic initial boundary value conditions by the finite difference method in spatial direction. Background on the discretization of the equations and the priori estimates; Existence of the attractors for the discrete system; Estimates of the upper bounds of Hausdorff and fractal dimensions for the attractors.

Regularity of the Attractor for 3-D Complex Ginzburg-Landau Equation

在这份报纸，为 3-D 建筑群 Ginzburg 四轮马车方程的全球引起注意的人的存在被考虑。由解决方案操作员的分解，这被显示出在 H i 的全球引起注意的人 A i () 实际上等于一个全球引起注意的人在 H j 的 j ()(i j，我， j = 1， 2， m ) 。

Sharp Threshold of Global Existence for the Klein-Gordon Equations with Critical Nonlinearity

在这篇论文，我们在场跨 constrained 在二种空间尺寸与批评非线性学习非线性的 Klein-Gordon 方程的 Cauchy 问题的变化方法。由构造跨 constrained 的一种类型，变化问题和进化的建立的所谓的跨 invariant manifolds 流动，我们建立它的全球存在和发作的锋利的阀值。而且，我们回答这个问题：如果答案全球性存在，起始的数据怎么小。

Random Attractors of Stochastic Non-Newtonian Fluids

The present paper investigates the asymptotic behavior of solutions for stochastic non-Newtonian fluids in a two-dimensional domain. Firstly, we prove the existence of random attractors AH （w） in H; Secondly, we prove the existence of random attractors Ay（w） in V. Then we verify regularity of the random attractors by showing that AH（W） = Ay（w）, which implies the smoothing effect of the fluids in the sense that solution becomes eventually more regular than the initial data.

A Class of Stable and Conservative Finite Difference Schemes for the Cahn-Hilliard Equation

In this paper, we propose a class of stable finite difference schemes for the initial-boundary value problem of the Cahn-Hilliard equation. These schemes are proved to inherit the total mass conservation and energy dissipation in the discrete level. The dissipation of the total energy implies boundness of the numerical solutions in the discrete H1 norm. This in turn implies boundedness of the numerical solutions in the maximum norm and hence the stability of the difference schemes. Unique existence of the numerical solutions is proved by the fixed-point theorem. Convergence rate of the class of finite difference schemes is proved to be O（h2 ＋ r2） with time step T and mesh size h. An efficient iterative algorithm for solving these nonlinear schemes is proposed and discussed in detail.

Stability of the Standing Waves for a Class of Coupled Nonlinear Klein-Gordon Equations

This paper deals with the standing waves for a class of coupled nonlinear Klein-Gordon equations with space dimension N ≥ 3, 0 〈 p, q 〈 2/N-2 and p ＋ q 〈 4/N. By using the variational calculus and scaling argument, we establish the existence of standing waves with ground state, discuss the behavior of standing waves as a function of the frequency ω and give the sufficient conditions of the stability of the standing waves with the least energy for the equations under study.

Global Random Attractors for the Stochastic Dissipative Zakharov Equations

The stochastic dissipative Zakharov equations with white noise are mainly investigated. The global random attractors endowed with usual topology for the stochastic dissipative Zakharov equations are obtained in the sense of usual norm. The method is to transform the stochastic equations into the corresponding partial differential equations with random coefficients by Ornstein-Uhlenbeck process. The crucial compactness of the global random attractors wiil be obtained by decomposition of solutions.

Stability and Instability of Schwarzschild-AdS for the Nonlinear Einstein-Klein-Gordon System

In this paper,we study the global behavior of solutions to the spherically symmetric(it means that the problem is 2+2 framework)coupled Nonlinear-Einstein-Klein-Gordon(NLEKG)system in the presence of a negative cosmological constant.We prove the well posedness of the NLEKG system in the Schwarzschild-AdS spacetimes and that the Schwarzschild-AdS spacetimes(the trivial black hole solutions of the EKG system for whichφ=0 identically)are asymptotically stable.Small perturbations of Schwarzschild-AdS initial data again lead to regular black holes,with the metric on the black hole exterior approaching a SchwarzschildAdS spacetime.Bootstrap argument on the black hole exterior,with the redshift effect and weighted Hardy inequalities playing the fundamental role in the analysis.Both integrated decay and pointwise decay estimates are obtained.

Local Stability to the Einstein-Euler System in Schwarzschild Space-time

We study the Schwarzschild spacetime solutions to the Einstein-Euler equations.In our analysis,we aim to show local stability under small perturbations.To resolve this problem,we use the Nash-Moser(-Hamilton)theorem.The work was originally developed for the nonrelativistic Euler-Poisson equations.

Solutions of Ginzburg-Landau Theory for Atomic Fermi Gases Near the BCS-BEC Crossover

We are concerned with a time-dependent Ginzburg-Landau equations come from the superfluid atomic Fermi-gases near the Feshbach resonance from the fermion-boson model. We obtain the global existence and uniqueness of solutions to the TDGL equations near the BCS-BEC crossover.