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Frontiers of Mathematics in China 2016年第6期11卷 1515-1532页

作者： Boling GUO Qiaoxin LI Institute of Applied Physics and Computational Mathematics Beijing 100088 China China Academy of Aerospace Aerodynamics Beijing 100074 China

We obtain the global smooth solution of a nonlinear SchrSdinger equations in atomic Bose-Einstein condensates with two-dimensional spaces. By using the Galerkin method and a priori estimates, we establish the global e... 详细信息

关键词： Schrodinger equation Galerkin method a priori estimate global smooth solution

global smooth solution of multi-dimensional non-homogeneous conservation laws

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Progress in Natural Science:Materials International 2004年第10期14卷 15-22页

作者： YANG Xiaozhou 1 and ZHANG Tong 2 (1.Department of Mathematics,Shantou University,Shantou515063,China 2.Institute of Mathematics,Chinese Academy of Sci-ences,Beijing100080,China) Dept. of Math. Shantou Univ. Shantou 515063 China Inst. of Math. Chinese Acad. of Sci. Beijing 100080 China

The initial value problem of multi-dimensional non-homogeneous conservation laws is studied and a sufficient condition of the existence of its global smooth solution is ***,three equivalent propositions of the existence of global smooth solution for multi-dimensional homogeneous scalar conservation laws are also *** global smooth solution is uniquely expressed by the global implicit function that is determined by a scalar equation,not by a system as usual methods do.

关键词： conservation laws global smooth solution global implicit function diffeomorphism

global smooth solution to the Incompressible Navier-Stokes-Landau-Lifshitz Equations

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Acta Mathematicae Applicatae Sinica 2023年第1期39卷 135-178页

作者： Guang-wu WANG You-de WANG School of Mathematics and Information Science Guangzhou UniversityGuangzhou 510006China Hua Loo-Keng Key Laboratory of Mathematics Institute of MathematicsAMSS and School of Mathematical ScienceUCASBeijing 100190China

In this paper, we will investigate the incompressible Navier-Stokes-Landau-Lifshitz equations, which is a system of the incompressible Navier-Stokes equations coupled with the Landau-Lifshitz-Gilbert equations. We will prove global existence of the smooth solution to the incompressible Navier-Stokes-Landau-Lifshitz equation with small initial data in T2or R2and R3.

关键词： incompressible Navier-Stokes-Landau-Lifshitz equations global smooth solution small initial data

FORMULA OF global smooth solution FOR NON-HOMOGENEOUS M-D CONSERVATION LAW WITH UNBOUNDED INITIAL VALUE

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Acta Mathematica Scientia 2015年第2期35卷 508-526页

作者：曹高伟胡凯杨小舟 Wuhan Institute of Physics and Mathematics CAS School of Mathematics and Statistics Southwest University

In this article, we prove the existence and obtain the expression of its solution formula of global smooth solution for non-homogeneous multi-dimensional（m-D） conservation law with unbounded initial value; our metho... 详细信息

关键词： solution formula non-homogeneous m-D conservation laws global smooth solution global implicit function

global smooth solution for the Quasi-linear Wave Equation

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Chinese Quarterly Journal of Mathematics 2005年第3期20卷 269-279页

作者： SONG Chang-ruing JIANG Shi-jing Department of Mathematics Zhongyuan Institute of Technology Zhengzhou 450007 China

In this paper, we study the Cauchy problem for the following quasi-linear wave equation utt-2kuxxt=β（ux^n）x, where k〉0 and β are real numbers, and n ≥ 2 is an integer. We prove that for any T〉0, the Cauchy problem admits a unique global smooth solution u∈C^∞（（0, T]; H^∞（R）） ∩ C（[0, T]; H^2（R）） ∩ C^1（[0, T]; L^2（R）） under suitable assumptions on the initial data.

关键词： quasi-linear wave equation Cauchy problem global smooth solution

Existence and Uniqueness of the global smooth solution to the Periodic Boundary Value Problem of Fractional Nonlinear Schr^dinger System

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Journal of Partial Differential Equations 2015年第2期28卷 95-119页

作者： WEI Gongming DONG Jing College of Science University of Shanghai for Science and TechnologyShanghai 200093 China.

In this paper, we study a class of coupled fractional nonlinear Schr^dinger system with periodic boundary condition. Using Galerkin method, the existence of global smooth solution is obtained. We also prove the unique... 详细信息

关键词： Nonlinear Schrodinger system global smooth solution Gagliardo-Nirenberg in-equality.

THE ASYMPTOTIC BEHAVIOR OF global smooth solutionS TO THE MACROSCOPIC MODELS FOR SEMICONDUCTORS

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Chinese Annals of Mathematics,Series B 2001年第2期22卷 195-210页

作者： HSIAOLING： WANGSHU AcademyofMathematicsandSystemsSciences theChineseAcademySciencesBeijing100080China DepartmentofMathematics HenanUniversityKaifeng475001ChinaandAcademyofMathematicsandSystemsSciencestheChineseAcademySciencesBeijing100080China.

The authors study the asymptotic behavior of the smooth solutions to the Cauchy problems for two macroscopic models (hydrodynamic and drift-diffusion models) for semiconductors and the related relaxation limit problem. First, it is proved that the solutions to these two systems converge to the unique stationary solution time asymptotically without the smallness assump- tion on doping profile. Then, very sharp estimates on the smooth solutions, independent of the relaxation time, are obtained and used to establish the zero relaxation limit.

关键词： Hydrodynamic model Semiconductors Asymptotic behavior global smooth solution Zero relaxation limit

EXISTENCE OF global smooth solutionS FOR TWO IMPORTANT NONSTRICTLY QUASILINEAR HYPERBOLIC SYSTEMS

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Acta Mathematica Scientia 1995年第1期15卷 48-57页

作者：朱长江赵会江 Wuhan Inst. of Math. Sci. Chin. Acad. of Sci. Wuhan 430071 China

In this paper,we study the global smooth solutions of the Cauchy problem for two important nonstrictly quasilinear hyperbolic systems.i.e.,the isentropic gas dynamics system in Euler coordinates (Ⅰ) and the rotational degeneracy of hyperbolic systems of conservation laws(Ⅱ).sufficient conditions which guarantee the existence of gloats smooth solutions of the Cauchy problems (Ⅰ) and (Ⅱ) are obtained by employing the characteristic method.

关键词： Nonstrictly quasilinear hyperbolic system a priori estimates global smooth solution

global EXISTENCE OF solutionS FOR A STRONGLY COUPLED REACTION-DIFFUSION SYSTEM

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Acta Mathematica Scientia 1998年第1期18卷 1-10页

作者：江成顺李海峰 Dept. of Math. Shandong Univ. Jinan 250100 China Zhengzhou Textile Institute Zhengzhou 450007 China

This paper is concerned with an Initial Boundary Value Problem (IBVP) for a strongly coupled semilinear reaction-diffusion system. By using the upper and lower solutions method and Leray-Schauder fixed point theorem and so on, the authors prove the global existence and uniqueness of a. smooth. solution for this IBVP under some appropriate conditions.

关键词： strongly coupled reaction-diffusion system global smooth solution upper and lower solutions Leray-Schauder fixed point theorem

(1+2)-Dimensional Radially Symmetric Wave Maps Revisit

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Chinese Annals of Mathematics,Series B 2022年第5期43卷 785-796页

作者： Yi ZHOU School of Mathematical Sciences Fudan UniversityShanghai 200433China

The author gives an alternative and simple proof of the global existence of smooth solutions to the Cauchy problem for wave maps from the(1+2)-dimensional Minkowski space to an arbitrary compact smooth Riemannian manifold without boundary, for arbitrary smooth, radially symmetric data. The author can also treat non-compact manifold under some additional assumptions which generalize the existing ones.

关键词： Cauchy problem Wave maps global smooth solution