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Existence of the solutions and the attractors for the large-scale atmospheric equations

Science china Earth Sciences 2006年第6期49卷 650-660页

作者： huang {1. {2. boling2.1. Department of mathematics, beijing normal University, beijing 1.0875, china 2. Institute of Applied Physics and Computational mathematics, beijing 1.0080, china Department of mathematics Beijing Normal University Beijing China Institute of Applied Physics and Computational mathematics Beijing China

In this paper, firstly, the proper function space is chosen, and the proper expression of the operators is introduced such that the complex large-scale atmospheric motion equations can be described by a simple and abstract equation, by which the definition of the weak solution of the atmospheric equations is made. Secondly, the existence of the weak solution for the atmospheric equations and the steady state equations is proved by using the Galerkin method. The existence of the non-empty global attractors for the atmospheric equations in the sense of the Chepyzhov-Vishik’s definition is obtained by constructing a trajectory attractor set of the atmospheric motion equations. The result obtained here is the foundation for studying the topological structure and the dynamical behavior of the atmosphere attractors. Moreover, the methods used here are also valid for studying the other atmospheric motion models.

关键词： atmosphere equations, weak solution, trajectory attractor, global attractor, equilibrium.

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On the Burgers-Ginzburg-Landau Equations

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Communications in Nonlinear Science and Numerical Simulation 1998年第3期3卷 143-147页

作者： boling {1. and {2. huang(Center of Nonlinear Studies. Institute of Applied Physics and Computationalmathematics, beijing, 1.0088. china)(Dept. of Math. beijing normal University. beijing 1.0875. china)E-mail: hhywsg@*** Center of Nonlinear Studies Inst. Appl. Phys. and Compl. Math. Beijing 100088 China Dept. of Math. Beijing Normal University Beijing 100875 China

In this paper we consider the Burger-Ginzburg-Landau equations. and provethe existence of the global attractor in with finite Hausdorff and fractaldimensions.

关键词： Burger-Ginzbur-Landau equations mild solution global attractor hausdorff and fractal dimensions

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The Cauchy problem for the stochastic generalized Benjamin-Ono equation

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Science china {1. 2021年第2期64卷 331-350页

作者： Wei Yan Jianhua huang {1. {2. College of mathematics and Information Science Henan Normal UniversityXinxiang 453007China College of Liberal Arts and Sciences National University of Defense TechnologyChangsha 410073China Institute of Applied Physics and Computational mathematics Beijing 100088China

The current paper is devoted to the Cauchy problem for the stochastic generalized Benjamin-Ono *** establishing the bilinear and trilinear estimates in some Bourgain spaces,we prove that the Cauchy problem for the stochastic generalized Benjamin-Ono equation is locally well-posed for the initial data u0(x,w)∈L^(2.(Ω;H^(s)(R))which is F0-measurable with s≥1.2.α/4 andΦ∈L2.,*** particular,whenα=1.we prove that it is globally well-posed for the initial data u0(x,w)∈L2.Ω;H1.R))which is F0-measurable andΦ∈L2.,*** key ingredients that we use in this paper are trilinear estimates,the Ito formula and the Burkholder-Davis-Gundy(BDG)inequality as well as the stopping time technique.

关键词： Cauchy problem stochastic generalized Benjamin-Ono equation bilinear estimate trilinear estimate

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