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
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
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 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.
