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global existence and Decay of Solutions for a Class of a Pseudo-Parabolic Equation with Singular Potential and Logarithmic Nonlocal Source

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Journal of Applied Mathematics and Physics 2024年第1期12卷 181-193页

作者： Xiaoxin Yang School of Mathematics and Statistics Changchun University of Science and Technology Changchun China

This article investigates the well posedness and asymptotic behavior of Neumann initial boundary value problems for a class of pseudo-parabolic equations with singular potential and logarithmic nonlinearity. By utilizing cut-off techniques and combining with the Faedo Galerkin approximation method, local solvability was established. Based on the potential well method and Hardy Sobolev inequality, derive the global existence of the solution. In addition, we also obtained the results of decay.

关键词： Nonlocal Parabolic Equation Singular Potential Logarithmic Nonlocal Source global existence Decay

global existence of the Solution for a Reduced Model of the Vectorial Quantum Zakharov System

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Journal of Applied Mathematics and Physics 2024年第2期12卷 533-542页

作者： Guiyu Yang College of Mathematical Science Zhejiang Normal University Zhejiang China College of Data Science Jiaxing University Zhejiang China

In this paper, we study the global existence of the smooth solution for a reduced quantum Zakharov system in two spatial dimensions. Using energy estimates and the logarithmic type Sobolev inequality, we show the glob... 详细信息

关键词： Quantum Zakharov System global existence Logarithmic Sobolev Inequality

Remarks on the global existence for Incompressible Navier-Stokes Equations

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Chinese Annals of Mathematics,Series B 2024年第4期45卷 529-536页

作者： Sheng WANG Zexian ZHANG Yi ZHOU Shanghai Center for Mathematical Sciences Fudan University School of Mathematics Science Fudan University

In this article, the authors use the special structure of helicity for the threedimensional incompressible Navier-Stokes equations to construct a family of finite energy smooth solutions to the Navier-Stokes equations... 详细信息

关键词： 17B40 17B50 Critical norm global existence Helicity Navier-Stokes euqations

global existence and time decay rates for the 3D bipolar compressible Navier-Stokes-Poisson system with unequal viscosities

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Science China Mathematics 2022年第4期65卷 731-752页

作者： Guochun Wu Yinghui Zhang Anzhen Zhang School of Mathematical Sciences Huaqiao UniversityQuanzhou362021China School of Mathematics and Statistics Guangxi Normal UniversityGuilin541004China

We consider the Cauchy problem for the three-dimensional bipolar compressible Navier-Stokes-Poisson system with unequal *** the assumption that the H_(3) norm of the initial data is small but its higher order derivatives can be arbitrarily large,the global existence and uniqueness of smooth solutions are obtained by an ingenious energy ***,if additionally,the H^(−s)(1/2≤s<3/2)or B^(−s)_(2,∞)(1/2

关键词： bipolar Navier-Stokes-Poisson global existence optimal decay rates

global existence of Strong Solutions for the Generalized Navier-Stokes Equations with Damping

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Acta Mathematicae Applicatae Sinica 2022年第3期38卷 627-634页

作者： Xiao-jing CAI Yan-jie ZHOU School of mathematics and statistics Beijing Technology and Business UniversityBeijing 100048China

This paper mainly focus on the global existence of the strong solutions for the generalized NavierStokes equations with damping. We obtain the global existence and uniqueness when α ≥5/4 for β ≥ 1 and when 1/2+β/... 详细信息

关键词： generalized Navier-Stokes equations damping global existence

global existence and Finite Time Blow-up for the m-Laplacian Parabolic Problem

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Acta Mathematica Sinica,English Series 2023年第8期39卷 1497-1524页

作者： Yue PANG Vicentiu D.RADULESCU Run Zhang XU College of Mathematical Sciences Harbin Engineering UniversityHarbin 150001P.R.China Faculty of Applied Mathematics AGH University of Science and Technology30-059 Krak´owPoland Department of Mathematics University of CraiovaStreet A.I.Cuza No.13200585 CraiovaRomania

In this paper,we consider an initial boundary value problem of m-Laplacian parabolic equation arising in various physical *** tackle this problem at three different initial energy *** the sub-critical initial energy,we obtain the blow-up result and estimate the lower and upper bounds of the blow-up *** the critical initial energy,we show the global existence,asymptotic behavior,finite time blow-up and the lower bound of the blow-up *** the sup-critical initial energy,we prove the finite time blow-up and estimate the lower and upper bounds of the blow-up time.

关键词： m-Laplacian parabolic equation blow-up blow-up time global existence

global existence and Extinction Behaviour for a Doubly Nonlinear Parabolic Equation with Logarithmic Nonlinearity

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Wuhan University Journal of Natural Sciences 2023年第2期28卷 99-105页

作者： LIU Dengming CHEN Ao School of Mathematics and Computational Science Hunan University of Science and TechnologyXiangtan 411201HunanChina

This paper is mainly focused on the global existence and extinction behaviour of the solutions to a doubly nonlinear parabolic equation with logarithmic nonlinearity. By making use of energy estimates method and a series of ordinary differential inequalities, the global existence of the solution is obtained. Moreover, we give the sufficient conditions on the occurrence(or absence)of the extinction behaviour.

关键词： global existence extinction behaviour doubly nonlinear parabolic equation logarithmic nonlinearity

global existence and Decay of Solution to Parabolic-Parabolic Keller-Segel Model in R^(d)

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Journal of Donghua University(English Edition) 2022年第1期39卷 85-94页

作者：钟文彬刘晓风 College of Science Donghua UniversityShanghai 201620China

We consider the global existence and decay of integral solutions to the parabolic-parabolic Keller-Segel system in *** the one hand,by Banach fixed point theorem and some properties of heat kernel,we prove the local existence and the global existence of integral solutions for the different initial data under some conditions that involve the size of the initial *** the other hand,in the case of global solutions,we obtain their optimal time decay by Gronwall’s lemma.

关键词： Keller-Segel system global existence integral solution local existence optimal time decay rate

Sharp Condition for global existence of Supercritical Nonlinear Schrodinger Equation with a Partial Confinement

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Acta Mathematicae Applicatae Sinica 2023年第1期39卷 202-210页

作者： Cheng-lin WANG Jian ZHANG University of Electronic Science and Technology of China Chengdu 611731China

We study the L^(2)-supercritical nonlinear Schrodinger equation(NLS) with a partial confinement,which is the limit case of the cigar-shaped model in Bose-Einstein condensate(BEC). By constructing a cross constrained variational problem and establishing the invariant manifolds of the evolution fow, we show a sharp condition for global existence.

关键词： nonlinear Schrodinger equation Bose-Einstein condensate cross-constrained variational problem global existence sharp condition