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A blow-up criterion FOR 3-D NON-RESISTIVE COMPRESSIBLE HEAT-CONDUCTIVE MAGNETOHYDRODYNAMIC EQUATIONS WITH INITIAL VACUUM

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Acta Mathematica Scientia 2012年第5期32卷 1883-1900页

作者：徐新英 School of Mathematical Sciences Capital Normal University School of Mathematical Sciences Xiamen University

In this paper,we prove a blow-up criterion of strong solutions to the 3-D viscous and non-resistive magnetohydrodynamic equations for compressible heat-conducting flows with initial *** blow-up criterion depends only on the gradient of velocity and the temperature,which is similar to the one for compressible Navier-Stokes equations.

关键词： compressible magnetohydrodynamics blow-up criterion vacuum zero resistivity heat-conducting flows

A blow-up criterion OF SPHERICALLY SYMMETRIC STRONG SOLUTIONS TO 3D COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH FREE BOUNDARY

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Acta Mathematica Scientia 2016年第4期36卷 1153-1166页

作者：孔慧慧李海梁张兴伟 School of Mathematical Sciences Capital Normal UniversityBeijing 100048China Institute of Applied Physics and Computational Mathematics Beijing 100088China

In this article, we consider the free boundary value problem of 3D isentropic compressible Navier-Stokes equations. A blow-up criterion in terms of the maximum norm of gradients of velocity is obtained for the spherically symmetric strong solution in terms of the regularity estimates near the symmetric center and the free boundary respectively.

关键词： blow-up criterion spherically symmetric free boundary compressible Navier- Stokes equations

A blow-up criterion OF STRONG SOLUTIONS TO THE QUANTUM HYDRODYNAMIC MODEL

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Acta Mathematica Scientia 2020年第3期40卷 795-804页

作者：王光武郭柏灵 School of Mathematics and Information Science Guangzhou UniversityGuangzhou 510006China Institute of Applied Physics and Computational Mathematics China Academy of Engineering PhysicsBeijing 100088China

In this article,we focus on the short time strong solution to a compressible quantum hydrodynamic *** establish a blow-up criterion about the solutions of the compressible quantum hydrodynamic model in terms of the gradient of the velocity,the second spacial derivative of the square root of the density,and the first order time derivative and first order spacial derivative of the square root of the density.

关键词： Compressible quantum hydrodynamic model blow-up criterion strong solution

REMARK ON THE blow-up criterion OF STRONG SOLUTIONS TO THE NAVIER-STOKES EQUATIONS IN MULTIPLIER SPACES

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Acta Mathematica Scientia 2010年第5期30卷 1413-1418页

作者： Sadek Gala Department of Mathematics University of Mostaganem

In this note, we prove that Xr （0 〈 r 〈 1） norm of the vorticity controls the blow-up phenomena of strong solutions to the Navier-Stokes equations in R3.

关键词： Navier-Stokes equation blow-up criterion a priori estimates

LOCAL EXISTENCE AND blow-up criterion OF 3D IDEAL MAGNETOHYDRODYNAMICS EQUATIONS

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Acta Mathematica Scientia 2018年第6期38卷 1759-1766页

作者： Jae-Myoung KIM Center for Mathematical Analysis & Computation Yonsei University

We investigate the local existence of smooth solutions of a 3D ideal magneto-hydrodynamics （MHD） equations in a bounded domain and give a blow-up criteria to thisequations with respect to vorticists.

关键词： ideal magnetohydrodynamics equations blow-up criterion bounded domain

On the blow-up criterion of Smooth Solutions to the MHD System in BMO Space

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Acta Mathematicae Applicatae Sinica 2006年第3期22卷 413-418页

作者： Bao-quan Yuan Academy of Mathematics & Systems Science Chinese Academy of Sciences Beijing 100080 China College of Mathematics and Informatics Henan Polytechnic University Jiaozuo 454000 China

In this paper we study the blow-up criterion of smooth solutions to the incompressible magnetohydrodynamics system in BMO space. Let （u（x,t）,b（x,t）） be smooth solutions in （0, T）. It is shown that the solution （u（x, t）, b（x, t）） can be extended beyond t = T if （u（x,t）, b（x, t）） ∈ L^1 （0, T; BMO） or the vorticity （rot u（x, t）, rot b（x, t）） ∈ L^1 （0, T; BMO） or the deformation （Def u（x, t）, Def b（x, t）） ∈ L^1 （0, T; BMO）.

关键词： Magneto-hydrodynamics system BMO space blow-up criterion

A Logarithmically Improved blow-up criterion for a Simplified Ericksen-Leslie System Modeling the Liquid Crystal Flows

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Journal of Partial Differential Equations 2015年第4期28卷 358-369页

作者： BAI Meng LIU Qiao ZHAO Jihong School of Mathematics and Statistics Zhaoqing UniversityZhaoqing 526061 China College of Mathematics and Computer Science Hunan Normal UniversityChangsha 410081 China College of Science Northwest A&F University Yangling 712100 China

In this paper, we prove a logarithmically improved blow-up criterion in terms of the homogeneous Besov spaces for a simplified 3D Ericksen-Leslie system modeling the hydrodynamic flow of nematic liquid crystal. The result shows that if a local smooth solution (u,d) satisfies with 0≤r<1 and s≥3, then the solution (u,d) can be smoothly extended beyond the time T.

关键词： Ericksen-Leslie system Navier-Stokes equations blow-up criterion

Local Well-Posedness and blow up criterion for the Inviscid Boussinesq System in Holder Spaces

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Journal of Partial Differential Equations 2012年第3期25卷 220-238页

作者： CUI Xiaona DOU Changsheng JIU Quansen School of Mathematical Sciences University of Chinese Academy of SciencesBeijing 100049China LCP Institute of Applied Physics and Computational MathematicsBeijing 100088China School of Mathematical Sciences Capital Normal UniversityBeijing 100048China

We prove the local in time existence and a blow up criterion of solution in the Holder spaces for the inviscid Boussinesq system in R-N,N >= 2, under the assumptions that the initial values theta(0),u(0) is an element... 详细信息

关键词： Inviscid Boussinesq system local well-posedness blow-up criterion EXISTENCE EQUATIONS REGULARITY

A Generalized blow up Criteria with One Component of Velocity for 3D Incompressible MHD System

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Chinese Annals of Mathematics,Series B 2024年第2期45卷 253-264页

作者： Bin HAN Xi XIONG Department of Mathematics Hangzhou Dianzi UniversityHangzhou 310018China

In this paper,the authors study the global regularity of the 3D magnetohydrodynamics system in terms of one velocity *** particular,they establish a new Prodi-Serrin type regularity criterion in the framework of weak ... 详细信息

关键词： MHD Regularity blow-up criterion