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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 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： Guangwu WANG Boling GUO 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

blow-up criterion OF SMOOTH SOLUTIONS TO THE MHD EQUATIONS IN BESOV SPACES

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Journal of Systems Science & Complexity 2005年第2期18卷 277-284页

作者： YUAN Baoquan (Graduate School, Chinese Academy of Engineering Physics P.O. Box 2101, Beijing 100088 Department of Applied Mathematics and Informatics, Henan Polytechnic University, Jiaozuo 454000, China. Graduate School Chinese Academy of Engineering Physics P.O. Box 2101 北京 100088

In this paper we discuss the logarithmic Sobolev inequalities in Besov spaces,and show their applications to the blow-up criterion of smooth solutions to the incompressible magneto-hydrodynamics equations.

关键词： logarithmic Sobolev inequalities magneto-hydrodynamics equations Besovspaces blow-up criterion

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

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

A blow-up criterion of strong solutions to the 2D compressible Navier-Stokes equations

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Science China Mathematics 2011年第1期54卷 105-116页

作者： SUN YongZhong ZHANG ZhiFei Department of Mathematics Nanjing University Nanjing 210093 China School of Mathematical Sciences Peking University Beijing 100871 China

We prove a blow-up criterion in terms of the upper bound of the density for the strong solution to 2D compressible Navier-Stokes equations in a bounded domain. The initial vacuum is allowed. The proof is based on the ... 详细信息

关键词： blow-up criterion compressible Navier-Stokes equations Lame system

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 ∫0^T｜｜u｜｜B∞,∞^-r^2/1-r＋｜｜▽d｜｜L∞^2/1＋1n（e＋｜｜u｜｜H^s＋｜｜▽d｜｜H^Sdt〈∞,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