Guo Boling

Partial regularity for two dimensional Landau-Lifshitz equations

It is proved that any weak solution to the initial value problem of two dimensional Landau-Lifshitz equation is unique and is smooth with the exception of at most finitely many points, provided that the weak solution has finite energy.

Global Regular Solutions for Landau-Lifshitz Equation

In this note, we prove that there exists a unique global regular solution for multidimensional Landau-Lifshitz equation if the gradient of solutions can be bounded in space L2(0, T; L∞). Moreover, for the two-dimensional radial symmetric Landau-Lifshitz equation with Neumann boundary condition in the exterior domain, this hypothesis in space L2(0, T; L∞) can be cancelled.

REMARKS ON THE GENERALIZED KADOMTSEV-PETVIASHVILI EQUATIONS AND TWO-DIMENSIONAL BENJAMIN-ONO EQUATIONS

In this paper, we investigate the well-posedness (existence and uniqueness) of the local solutions for the Cauchy problem of generalized Kadomtsev-Petviashvili equations and Benjamin-Ono equations: (ut + αuxxx + βHuxx + upux)x + ϵuyy = 0. If p ≥ 4, then the solution blows up in finite time for suitable initial data.

On the suitable weak solutions to the Boussinesq equations in a bounded domain

In this paper we construct the suitable weak solution for the initial-boundary value problem of the Boussinesq equations and obtain some properties for these solutions. Also in the case of a two dimensional space the uniqueness of weak solution is proved.

Attractors of derivative complex Ginzburg-Landau equation in unbounded domains

The Ginzburg-Landau-type complex equations are simplified mathematical models for various pattern formation systems in mechanics, physics, and chemistry. In this paper, the derivative complex Ginzburg-Landau (DCGL) equation in an unbounded domain Ω ⊂ ℝ2 is studied. We extend the Gagliardo-Nirenberg inequality to the weighted Sobolev spaces introduced by S. V. Zelik. Applied this Gagliardo-Nirenberg inequality of the weighted Sobolev spaces and based on the technique for the semi-linear system of parabolic equations which has been developed by M. A. Efendiev and S. V. Zelik, the global attractor in the corresponding phase space is constructed, the upper bound of its Kolmogorov’s ɛ-entropy is obtained, and the spatial chaos of the attractor for DCGL equation in ℝ2 is detailed studied.

LONG-TIME BEHAVIOR FOR THE EQUATION OF FINITE-DEPTH FLUIDS

AbstractIn this paper we study the Cauchy problem for the generalized equation of finite-depth fluidsn

Global attractors for the initial value problems of Cohn-Hilliard equations on compact manifolds

partial _t u - G(partial _x^2 u) - partial _x left( {frac{{u^p }}{p}} right) = 0

Isometric decomposition operators, function spaces Ep,qλ and applications to nonlinear evolution equations

n whereG(·) is a singular integral, andp is an integer larger than 1. We obtain the long time behavior of the fundamental solution of linear problem, and prove that the solutions of the nonlinear problem with small initial data forn