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Global solution for quantum Zakharov equations

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Applied Mathematics and Mechanics(English Edition) 2017年第4期38卷 603-616页

作者： Shujun YOU boling guo Department of Mathematics Huaihua University Huaihua 418008 Hunan Province China Institute of Applied Physics and Computational Mathematics Beijing 100088 China

The initial value problem for the quantum Zakharov equation in three di- mensions is studied. The existence and uniqueness of a global smooth solution are proven with coupled a priori estimates and the Galerkin method.

关键词： quantum Zakharov equation initial value problem global solution

Local Well-posedness of the Derivative Schrödinger Equation in Higher Dimension for Any Large Data

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Chinese Annals of Mathematics,Series B 2022年第6期43卷 977-998页

作者： boling guo Zhaohui HUO Institute of Applied Physics and Computational Mathematics P.O.Box 8009Beijing 100088China Institute of Mathematics Academy of Mathematics and Systems ScienceCASBeijing 100190China Hua Loo-Keng Key Laboratory of Mathematics Chinese Academy of SciencesBeijing 100190China

In this paper,the authors consider the local well-posedness for the derivative Schrödinger equation in higher dimension ut-iΔu+|u|^(2)(→γ·▽u)+u^(2)(→λ·▽-u)=0,(x,t)∈R^(n)×R,→γ,→λ∈R^(n);n≥2 It is shown that the Cauchy problem of the derivative Schrödinger equation in higher dimension is locally well-posed in H^(s)(R^(n))(s>n/2)for any large initial *** this result can compare with that in one dimension except for the endpoint space H^(n/2).

关键词： Well-posedness Derivative Schrödinger equation in higher dimension Short-time Xs b Large initial data

Local regularity properties for ID mixed nonlinear Schrodinger equations on half-line

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Frontiers of Mathematics in China 2020年第6期15卷 1121-1142页

作者： boling guo Jun WU Institute of Applied Physics and Computational Mathematics Beijing 100088China Graduate School of China Academy of Engineering Physics Beijing 100088China

The main purpose of this paper is to consider the initial-boundary value problem for the 1D mixed nonlinear Schrodinger equation ut=iαu_(xx)+βu^(2)u_(x)+γ|u|^(2)u_(x)+i|u|^(2)u on the half-line with inhomogeneous boundary *** combine Laplace transform method with restricted norm method to prove the local well-posedness and continuous dependence on initial and boundary data in low regularity Sobolev ***,we show that the nonlinear part of the solution on the half-line is smoother than the initial data.

关键词： Mixed nonlinear Schrodinger(MNLS)equations initial-boundary value problem(IBVP) Bourgain spaces local well-posedness

Long-time asymptotics for the initial-boundary value problem of coupled Hirota equation on the half-line

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Science China Mathematics 2021年第1期64卷 81-110页

作者： Nan Liu boling guo Institute of Applied Physics and Computational Mathematics Beijing100088China

The object of this work is to investigate the initial-boundary value problem for coupled Hirota equation on the *** show that the solution of the coupled Hirota equation can be expressed in terms of the solution of a 3×3 matrix Riemann-Hilbert problem formulated in the complex *** relevant jump matrices are explicitly given in terms of the matrix-valued spectral functions s(k)and S(k)that depend on the initial data and boundary values,***,applying nonlinear steepest descent techniques to the associated 3×3 matrix-valued Riemann-Hilbert problem,we can give the precise leading-order asymptotic formulas and uniform error estimates for the solution of the coupled Hirota equation.

关键词： coupled Hirota equation initial-boundary value problem long-time asymptotics

GEVREY CLASS REGULARITY AND APPROXIMATE INERTIAL MANIFOLDS FOR THE NEWTON-BOUSSINESQ EQUATIONS

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Chinese Annals of Mathematics,Series B 1998年第2期19卷 179-188页

作者： guo boling WANG BIXIANG Institute of Applied Physics and Computational Mathematics P.O. Box 8009 Beijing 100088 China Department of Applied Mathematics Tsinghua University Beijing 100084 China

The authors show the Gevrey class regularity of the solutions for the two-dimensional Newton-Boussinesq Equations. Based on this fact, an approximate inertial manifold for the system is constructed, which attracts ... 详细信息

关键词： Gevrey class regularity Global attractor Approximate inertial manifold Newton-Boussinesq Equation

Implicit finite difference method for fractional percolation equation with Dirichlet and fractional boundary conditions

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Applied Mathematics and Mechanics(English Edition) 2016年第3期37卷 403-416页

作者： boling guo Qiang XU Zhe YIN Institute of Applied Physics and Computational Mathematics Beijing 100088 China School of Mathematical Sciences Shandong Normal University Jinan 250014 China

An implicit finite difference method is developed for a one-dimensional frac- tional percolation equation （FPE） with the Dirichlet and fractional boundary conditions. The stability and convergence are discussed for two special cases, i.e., a continued seep- age flow with a monotone percolation coefficient and a seepage flow with the fractional Neumann boundary condition. The accuracy and efficiency of the method are checked with two numerical examples.

关键词： fractional percolation equation (FPE) Riemann-Liouville derivative frac-tional boundary condition finite difference method stability and convergence Toeplitzmatrix

Existence and blow-up of the solutions to the viscous quantum magnetohydrodynamic nematic liquid crystal model

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Science China Mathematics 2019年第3期62卷 469-508页

作者： Guangwu Wang boling guo School of Mathematics and Information Science Guangzhou University Graduate School of China Academy of Engineering Physics Institute of Applied Physics and Computational Mathematics China Academy of Engineering Physics

In this paper, we investigate the coupled viscous quantum magnetohydrodynamic equations and nematic liquid crystal equations which describe the motion of the nematic liquid crystals under the magnetic field and the quantum effects in the two-dimensional case. We prove the existence of the global finite energy weak solutions by use of a singular pressure close to vacuum. Then we obtain the local-in-time existence of the smooth solution. In the final, the blow-up of the smooth solutions is studied. The main techniques are Faedo-Galerkin method, compactness theory, Arzela-Ascoli theorem and construction of the functional differential inequality.

关键词： viscous quantum magnetohydrodynamic equations nematic liquid crystal global weak solution singular pressure smooth solution blow-up

Global weak solutions to a phase-field model for motion of grain boundaries

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Applied Mathematics and Mechanics(English Edition) 2022年第11期43卷 1777-1792页

作者： Zixian ZHU boling guo Shaomei FANG Department of Mathematics Shanghai UniversityShanghai 200444China Institute of Applied Physics and Computational Mathematics Beijing 100088China College of Mathematics and Information South China Agricultural UniversityGuangzhou 510642China

We employ the Galerkin method to prove the global existence of weak solutions to a phase-field model which is suitable to describe a sort of interface motion driven by configurational *** higher-order derivative of unknown S exists in the sense of local weak derivatives since it may be not summable over the original open *** existence proof is valid in the one-dimensional case.

关键词： solid-solid phase transition phase-field model Galerkin method weak solutions

Well-posedness for compressible Rayleigh-Benard convection

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Frontiers of Mathematics in China 2013年第6期8卷 1253-1264页

作者： Dongfen BIAN boling guo The Graduate School of China Academy of Engineering Physics Beijing 100088 China Institute of Applied Physics and Computational Mathematics Beijing 100088 China

The Rayleigh-B^nard convection is a classical problem in fluid dynamics. In this paper, we are concerned with the well-posedness for the compressible Rayleigh-B^nard convection in a bounded domain Ω R2. We prove the local well-posedness of the system with appropriate initial data. This is the result concerning compressible Rayleigh-B^nard convection, before only results about incompressible Rayleigh-B^nard convection were done.

关键词： Compressible Rayleigh-BSnard convection well-posedness energy method