半平面上的非等熵MHD方程组的不可压极限  

Incompressible Limit of the Non-isentropic Magnetohydrodynamic Equations in the Half Plane

作　　者：徐自立[1,2] 王术[1] 

机构地区：[1]北京工业大学应用数理学院,北京100124 [2]中州大学信息工程学院,郑州450044

出　　处：《北京工业大学学报》2015年第2期308-315,共8页Journal of Beijing University of Technology

基　　金：国家自然科学基金资助项目(11371042);北京市自然科学基金资助项目(1132006)

摘　　要：为了研究在半平面上速度场具有Dirichlet条件,且磁场具有完美物理传导条件的非等熵的MHD方程组的不可压极限,采用了能量方法和一般正则性理论,并且通过Schauder不动点理论证明解的存在性,通过Gronwall不等式证明了解的唯一性,这样在具有好始值的前提下,在小时间区间上建立了不依赖于小马赫数ε∈(0,1]的一致估计,其中也包括了在边界法线方向上的速度的高阶导数的估计.最终得出了MHD方程组的局部解的存在性和唯一性.To study the incompressible limit of the non-isentropic magnetohydrodynamic （ MHD ） equations with the Dirichlet condition for velocity and perfectly conducting boundary condition for magnetic field in the half plane, the energy method and the general regularity theory are implied, and the existence of solution follows from the Schauder fixed-point theorem and the uniqueness from the Gronwall inequality. Then the uniform estimates in the Mach number, which exclude the estimate of high-order derivatives of the velocity in the normal directions to the boundary, are estimated within a short time interval independent of Mach number ε∈（0,1], provided that the initial data are well-prepared. Finally, the global existence and uniqueness of solution for MHD equations are obtained.

关 键 词：小马赫数 非等熵MHD方程组 边界区域 

分 类 号：O175.29[理学—数学]