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Acta Mathematica Scientia 2021年第5期41卷 1503-1536页

作者： Fucai LI Zhipeng ZHANG Department of Mathematics Nanjing UniversityNanjing 210093China Institute of Applied Physics and Computational Mathematics Beijing 100088China

We investigate the uniform regularity and zero kinematic viscosity-magnetic diffusion limit for the incompressible viscous magnetohydrodynamic equations with the navier boundary conditions on the velocity and perfectly conducting conditions on the magnetic field in a smooth bounded domain Ω⊂R^(3).It is shown that there exists a unique strong solution to the incompressible viscous magnetohydrodynamic equations in a finite time interval which is independent of the viscosity coefficient and the magnetic diffusivity *** solution is uniformly bounded in a conormal Sobolev space and W^(1,∞)(Ω)which allows us to take the zero kinematic viscosity-magnetic diffusion ***,we also get the rates of convergence in L^(∞)(0,T;L^(2)),L^(∞)(0,T;W^(1,p))(2≤p0.

关键词： incompressible viscous MHD equations ideal incompressible MHD equations navier boundary conditions zero kinematic viscosity-magnetic diffusion limit

Weighted polyharmonic equation with navier boundary conditions in a half space

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Science China Mathematics 2017年第3期60卷 491-510页

作者： ZHUO Ran Department of Mathematical Sciences Huanghuai University Zhumadian 463000 China Department of Mathematical Sciences Yeshiva UniversityNew York NY 10033 USA

We study positive solutions of the following polyharmonic equation with Hardy weights associated to navier boundary conditions on a half space：where rn is any positive integer satisfying 0 〈 2m 〈 n. We first prove that the positive solutions of （0.1） are super polyharmonic, i.e.,where x＊ = （x1,... ,Xn-1, --Xn） is the reflection of the point x about the plane Rn-1. Then, we use the method of moving planes in integral forms to derive rotational symmetry and monotonicity for the positive solution of （0.3）, in which α can be any real number between 0 and n. By some Pohozaev type identities in integral forms, we prove a Liouville type theorem--the non-existence of positive solutions for （0.1）.

关键词： navier boundary conditions half space super polyharmonic equivalence integral equation rotational symmetry non-existence

THE COMBINED INVISCID AND NON-RESISTIVE LIMIT FOR THE NONHOMOGENEOUS INCOMPRESSIBLE MAGNETOHYDRODYNAMIC EQUATIONS WITH navier boundary conditions

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Acta Mathematica Scientia 2018年第6期38卷 1655-1677页

作者： Zhipeng ZHANG Institute of Applied Physics and Computational Mathematics Beijing 100088 China Department of Mathematics Nanjing University Nanjing 210093 China

In this paper, we establish the existence of the global weak solutions for the non-homogeneous incompressible magnetohydrodynamic equations with navier boundary condi-tions for the velocity field and the magnetic field in a bounded domain Ω R^3. Furthermore,we prove that as the viscosity and resistivity coefficients go to zero simultaneously, these weaksolutions converge to the strong one of the ideal nonhomogeneous incompressible magneto-hydrodynamic equations in energy space.

关键词： nonhomogeneous incompressible MHD equations navier boundary conditions Inviscid and non-resistive limit

LOCATION OF THE BLOW UP POINT FOR POSITIVE SOLUTIONS OF A BIHARMONIC EQUATION INVOLVING NEARLY CRITICAL EXPONENT

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Acta Mathematica Scientia 2005年第2期25卷 283-295页

作者：耿堤 Department of Mathematics South China Normal University Guangzhou 510631China

In this paper a semilinear biharmonic problem involving nearly critical growth with navier boundary condition is considered on an any bounded smooth domain. It is proved that positive solutions concentrate on a point in the domain, which is also a critical point of the Robin’s function corresponding to the Green’s function of biharmonic operator with the same boundary condition. Similar conclusion has been obtained in [6] under the condition that the domain is strictly convex.

关键词： Biharmonic operator navier boundary conditions asymptotic behavior critical exponents Green's function