This paper verifies the low Mach number limit of the non-isentropic compressible magnetohydrodynamic(MHD)equations with or without the magnetic diffusion in a three-dimensional bounded domain when the temperature vari...This paper verifies the low Mach number limit of the non-isentropic compressible magnetohydrodynamic(MHD)equations with or without the magnetic diffusion in a three-dimensional bounded domain when the temperature variation is large but finite.The uniform estimates of strong solutions are established in a short time interval independent of the Mach number,provided that the slip boundary condition for the velocity and the Neumann boundary condition for the temperature are imposed and the initial data is well-prepared.展开更多
In this paper, we investigate the large-time behavior of strong solutions to the Cauchy problem for one-dimensional compressible isentropic magnetohydrodynamic equations near a stable equilibrium. The difference betwe...In this paper, we investigate the large-time behavior of strong solutions to the Cauchy problem for one-dimensional compressible isentropic magnetohydrodynamic equations near a stable equilibrium. The difference between the one-dimensional and multi-dimensional cases is a feature for compressible flows and also brings new difficulties. In contrast to the multi-dimensional case, the decay rates of nonlinear terms may not be faster than linear terms in dimension one. To handle this, we shall present a new energy estimate in terms of a combination of the solutions with small initial data. We aim to establish the sharp upper and lower bounds on the L^(2)-decay rates of the solutions and all their spatial derivatives when the initial perturbation is small in L^(1)(R) ∩ H^(2)(R). It is worth noticing that there is no decay loss for the highest-order spatial derivatives of the solutions so that the large-time behavior for the hyperbolic-parabolic system is exactly sharp. As a byproduct, the above result is also valid for compressible Navier-Stokes equations. Our approach is based on various interpolation inequalities, energy estimates, spectral analysis, and Fourier time-splitting and high-low frequency decomposition methods.展开更多
Regularity criteria in terms of bounds for the pressure are derived for the 3D MHD equations in a bounded domain with slip boundary conditions.A list of three regularity criteria is shown.
We are concerned with singularity formation of strong solutions to the two-dimensional(2D)full compressible magnetohydrodynamic equations with zero resistivity in a bounded domain.By energy method and critical Sobolev...We are concerned with singularity formation of strong solutions to the two-dimensional(2D)full compressible magnetohydrodynamic equations with zero resistivity in a bounded domain.By energy method and critical Sobolev inequalities of logarithmic type,we show that the strong solution exists globally if the temporal integral of the maximum norm of the deformation tensor is bounded.Our result is the same as Ponce’s criterion for 3D incompressible Euler equations.In particular,it is independent of the magnetic field and temperature.Additionally,the initial vacuum states are allowed.展开更多
In this article, regularity criteria for the 3D magnetohydrodynamic equations are investigated. Some sufficient integrability conditions on two components or the gradient of two components of u ＋ B and u - B in Morre...In this article, regularity criteria for the 3D magnetohydrodynamic equations are investigated. Some sufficient integrability conditions on two components or the gradient of two components of u ＋ B and u - B in Morrey-Campanato spaces are obtained.展开更多
We investigate initial-boundary-value problem for three-dimensional magnetohydrodynamic （MHD） system of compressible viscous heat-conductive flows and the three-dimensional full compressible Navier-Stokes equations....We investigate initial-boundary-value problem for three-dimensional magnetohydrodynamic （MHD） system of compressible viscous heat-conductive flows and the three-dimensional full compressible Navier-Stokes equations. We establish a blowup criterion only in terms of the derivative of velocity field, similar to the Beale^Kato-Majda type criterion for compressible viscous barotropic flows by Huang et al. （2011）. The results indicate that the nature of the blowup for compressible MHD models of viscous media is similar to the barotropic compressible Navier-Stokes equations and does not depend on further sophistication of the MHD model, in particular, it is independent of the temperature and magnetic field. It also reveals that the deformation tensor of the velocity field plays a more dominant role than the electromagnetic field and the temperature in regularity theory. Especially, the similar results also hold for compressible viscous heat-conductive Navier-Stokes flows, which extend the results established by Fan et al. （2010）, and I-Iuang and Li （2009）. In addition, the viscous coefficients are only restricted by the physical conditions in this paper.展开更多
We prove the existence and uniqueness of global strong solutions to the Cauchy problem of the three-dimensional magnetohydrodynamic equations in R3 when initial data are helically symmetric. Moreover, the large-time b...We prove the existence and uniqueness of global strong solutions to the Cauchy problem of the three-dimensional magnetohydrodynamic equations in R3 when initial data are helically symmetric. Moreover, the large-time behavior of the strong solutions is obtained simultaneously.展开更多
In this paper, we consider the three dimensional compressible viscous magnetohydrodynamic equations（MHD） with the external potential force. We first derive the corresponding non-constant stationary solutions. Next, ...In this paper, we consider the three dimensional compressible viscous magnetohydrodynamic equations（MHD） with the external potential force. We first derive the corresponding non-constant stationary solutions. Next, we show global wellposedness of the initial value problem for the three dimensional compressible viscous magnetohydrodynamic equations, provided that the initial data is close to the stationary solution. Finally, based on the elaborate energy estimates for the nonlinear system and L^p-L^q decay estimates of the linearized equation, we show the optimal convergence rates of the solution in L^q-norm with 2≤q≤6 and its first derivative in L^2-norm when the initial perturbation is bounded in L^p-norm with 1≤p〈6/5.展开更多
In this paper,the global existence of the classical solution to the vacuum free boundary problem of full compressible magnetohydrodynamic equations with large initial data and axial symmetry is studied.The solutions t...In this paper,the global existence of the classical solution to the vacuum free boundary problem of full compressible magnetohydrodynamic equations with large initial data and axial symmetry is studied.The solutions to the system(1.6)–(1.8) are in the class of radius-dependent solutions,i.e.,independent of the axial variable and the angular variable.In particular,the expanding rate of the moving boundary is obtained.The main difficulty of this problem lies in the strong coupling of the magnetic field,velocity,temperature and the degenerate density near the free boundary.We overcome the obstacle by establishing the lower bound of the temperature by using different Lagrangian coordinates,and deriving the uniform-in-time upper and lower bounds of the Lagrangian deformation variable r;by weighted estimates,and also the uniform-in-time weighted estimates of the higher-order derivatives of solutions by delicate analysis.展开更多
In this paper we propose a development of the finite difference method,called the tailored finite point method,for solving steady magnetohydrodynamic(MHD)duct flow problems with a high Hartmann number.When the Hartman...In this paper we propose a development of the finite difference method,called the tailored finite point method,for solving steady magnetohydrodynamic(MHD)duct flow problems with a high Hartmann number.When the Hartmann number is large,the MHD duct flow is convection-dominated and thus its solution may exhibit localized phenomena such as the boundary layer.Most conventional numerical methods can not efficiently solve the layer problem because they are lacking in either stability or accuracy.However,the proposed tailored finite point method is capable of resolving high gradients near the layer regions without refining the mesh.Firstly,we devise the tailored finite point method for the scalar inhomogeneous convectiondiffusion problem,and then extend it to the MHD duct flow which consists of a coupled system of convection-diffusion equations.For each interior grid point of a given rectangular mesh,we construct a finite-point difference operator at that point with some nearby grid points,where the coefficients of the difference operator are tailored to some particular properties of the problem.Numerical examples are provided to show the high performance of the proposed method.展开更多
基金supported by National Natural Science Foundation of China(Grant Nos.11971477,12131007 and 11761141008)the Fundamental Research Funds for the Central Universitiesthe Research Funds of Renmin University of China(Grant No.18XNLG30)。
文摘This paper verifies the low Mach number limit of the non-isentropic compressible magnetohydrodynamic(MHD)equations with or without the magnetic diffusion in a three-dimensional bounded domain when the temperature variation is large but finite.The uniform estimates of strong solutions are established in a short time interval independent of the Mach number,provided that the slip boundary condition for the velocity and the Neumann boundary condition for the temperature are imposed and the initial data is well-prepared.
基金supported by Guangdong Basic and Applied Basic Research Foundation(Grant No.2019A1515110733)National Natural Science Foundation of China(Grant Nos.11971496 and 11972384)+1 种基金National Key R&D Program of International Collaboration(Grant No.2018YFE9103900)National Key R&D Program of China(Grant No.2020YFA0712500)。
文摘In this paper, we investigate the large-time behavior of strong solutions to the Cauchy problem for one-dimensional compressible isentropic magnetohydrodynamic equations near a stable equilibrium. The difference between the one-dimensional and multi-dimensional cases is a feature for compressible flows and also brings new difficulties. In contrast to the multi-dimensional case, the decay rates of nonlinear terms may not be faster than linear terms in dimension one. To handle this, we shall present a new energy estimate in terms of a combination of the solutions with small initial data. We aim to establish the sharp upper and lower bounds on the L^(2)-decay rates of the solutions and all their spatial derivatives when the initial perturbation is small in L^(1)(R) ∩ H^(2)(R). It is worth noticing that there is no decay loss for the highest-order spatial derivatives of the solutions so that the large-time behavior for the hyperbolic-parabolic system is exactly sharp. As a byproduct, the above result is also valid for compressible Navier-Stokes equations. Our approach is based on various interpolation inequalities, energy estimates, spectral analysis, and Fourier time-splitting and high-low frequency decomposition methods.
基金J.Fan is partially supported by NSFC(No.11171154)Ju is supported by NSFC(Grant Nos.12071044,12131007).
文摘Regularity criteria in terms of bounds for the pressure are derived for the 3D MHD equations in a bounded domain with slip boundary conditions.A list of three regularity criteria is shown.
基金partially supported by National Natural Science Foundation of China(Nos.11901474,12371227)。
文摘We are concerned with singularity formation of strong solutions to the two-dimensional(2D)full compressible magnetohydrodynamic equations with zero resistivity in a bounded domain.By energy method and critical Sobolev inequalities of logarithmic type,we show that the strong solution exists globally if the temporal integral of the maximum norm of the deformation tensor is bounded.Our result is the same as Ponce’s criterion for 3D incompressible Euler equations.In particular,it is independent of the magnetic field and temperature.Additionally,the initial vacuum states are allowed.
基金supported in part by the NNSF of China (11101144,11171377)Research Initiation Project for High-level Talents (201031) of North China University of Water Resources and Electric Power
文摘In this article, regularity criteria for the 3D magnetohydrodynamic equations are investigated. Some sufficient integrability conditions on two components or the gradient of two components of u ＋ B and u - B in Morrey-Campanato spaces are obtained.
基金supported by National Natural Science Foundation of China(Grant Nos.11171236 and 71372189)Program for Changjiang Scholars and Innovative Research Team in University(Grant No.IRT1273)+1 种基金Sichuan Youth Science and Technology Foundation(Grant No.2014JQ0003)China Postdoctoral Science Foundation(Grant No.2013M542285)
文摘We investigate initial-boundary-value problem for three-dimensional magnetohydrodynamic （MHD） system of compressible viscous heat-conductive flows and the three-dimensional full compressible Navier-Stokes equations. We establish a blowup criterion only in terms of the derivative of velocity field, similar to the Beale^Kato-Majda type criterion for compressible viscous barotropic flows by Huang et al. （2011）. The results indicate that the nature of the blowup for compressible MHD models of viscous media is similar to the barotropic compressible Navier-Stokes equations and does not depend on further sophistication of the MHD model, in particular, it is independent of the temperature and magnetic field. It also reveals that the deformation tensor of the velocity field plays a more dominant role than the electromagnetic field and the temperature in regularity theory. Especially, the similar results also hold for compressible viscous heat-conductive Navier-Stokes flows, which extend the results established by Fan et al. （2010）, and I-Iuang and Li （2009）. In addition, the viscous coefficients are only restricted by the physical conditions in this paper.
基金Supported by the National Natural Science Foundation of China(No.11071195)partially supported by the National Natural Science Foundation of China(No.11071195)a research grant at the Northwest University
文摘We prove the existence and uniqueness of global strong solutions to the Cauchy problem of the three-dimensional magnetohydrodynamic equations in R3 when initial data are helically symmetric. Moreover, the large-time behavior of the strong solutions is obtained simultaneously.
基金Supported by the National Natural Science Foundation of China(11671134)
文摘In this paper, we consider the three dimensional compressible viscous magnetohydrodynamic equations（MHD） with the external potential force. We first derive the corresponding non-constant stationary solutions. Next, we show global wellposedness of the initial value problem for the three dimensional compressible viscous magnetohydrodynamic equations, provided that the initial data is close to the stationary solution. Finally, based on the elaborate energy estimates for the nonlinear system and L^p-L^q decay estimates of the linearized equation, we show the optimal convergence rates of the solution in L^q-norm with 2≤q≤6 and its first derivative in L^2-norm when the initial perturbation is bounded in L^p-norm with 1≤p〈6/5.
基金supported by National Natural Science Foundation of China(Grant Nos.11971477,11761141008,11601128 and 11671319)the Fundamental Research Funds for the Central Universities+3 种基金the Research Funds of Renmin University of China(Grant No.18XNLG30)Beijing Natural Science Foundation(Grant No.1182007)Doctor Fund of Henan Polytechnic University(Grant No.B2016-57)completed when Yaobin Ou visited Brown University under the support of the China Scholarship Council(Grant No.201806365010)。
文摘In this paper,the global existence of the classical solution to the vacuum free boundary problem of full compressible magnetohydrodynamic equations with large initial data and axial symmetry is studied.The solutions to the system(1.6)–(1.8) are in the class of radius-dependent solutions,i.e.,independent of the axial variable and the angular variable.In particular,the expanding rate of the moving boundary is obtained.The main difficulty of this problem lies in the strong coupling of the magnetic field,velocity,temperature and the degenerate density near the free boundary.We overcome the obstacle by establishing the lower bound of the temperature by using different Lagrangian coordinates,and deriving the uniform-in-time upper and lower bounds of the Lagrangian deformation variable r;by weighted estimates,and also the uniform-in-time weighted estimates of the higher-order derivatives of solutions by delicate analysis.
基金supported by the National Science Council of Taiwan under the Grant NSC 97-2115-M-008-015-MY2.
文摘In this paper we propose a development of the finite difference method,called the tailored finite point method,for solving steady magnetohydrodynamic(MHD)duct flow problems with a high Hartmann number.When the Hartmann number is large,the MHD duct flow is convection-dominated and thus its solution may exhibit localized phenomena such as the boundary layer.Most conventional numerical methods can not efficiently solve the layer problem because they are lacking in either stability or accuracy.However,the proposed tailored finite point method is capable of resolving high gradients near the layer regions without refining the mesh.Firstly,we devise the tailored finite point method for the scalar inhomogeneous convectiondiffusion problem,and then extend it to the MHD duct flow which consists of a coupled system of convection-diffusion equations.For each interior grid point of a given rectangular mesh,we construct a finite-point difference operator at that point with some nearby grid points,where the coefficients of the difference operator are tailored to some particular properties of the problem.Numerical examples are provided to show the high performance of the proposed method.
