MHD方程组解的适定性及非线性稳定性
发布时间：2018-10-25 07:22
【摘要】：本文从Euler方程出发,考虑流体粘性可以提出Navier-Stokes方程,当研究磁场作用时提出了磁流体力学(magnetohydrodynamic,简称MHD)方程。磁流体力学系统描述粘性或无粘性,可压缩或不可压缩导电流体与磁场间的相互作用。MHD模型在诸如地球物理学,天文学,工程学等许多领域都有广泛的应用,它是描述导电流体与磁场间相互作用的最简单的模型之一。本文考虑在无限长旋转圆柱内带有科氏力的理想不可压缩MHD流的运动,得到了带有科氏力的MHD流定态解的稳定性和不稳定性判据;另外,我们研究有界区域中MHD方程组弱解的适定性问题,利用Galerkin方法和先验估计,证明了当(u0,B0)∈((Wm,p(Ω))2×Wm,p)(Ω)时,弱解(u(.,t),B(.,t))∈((Wm,p(Ωm,(Ω))2 × 的存在唯一性及其对初值的连续依赖性;进一步,我们研究了N维有界区域中理想不可压缩MHD方程组强解的适定性问题,利用Galerkin方法和先验估计,证明了当(u0,B0)∈((Hm(Ω))N×(Hm(Ω))N)时,强解(u(·,t),B(·,t))∈((Hm Ω))N×(Hm(Ω)N)的存在唯一性及其对初值的连续依赖性。
[Abstract]:Based on the Euler equation and considering the viscosity of the fluid, the Navier-Stokes equation can be proposed in this paper. When the magnetic field is studied, the magnetohydrodynamic, equation is proposed. The MHD model is widely used in many fields such as geophysics, astronomy, engineering and so on. It is one of the simplest models to describe the interaction between conductive fluid and magnetic field. In this paper, the motion of an ideal incompressible MHD flow with Coriolis force in an infinite rotating cylinder is considered, and the stability and instability criteria of the stationary solution of the MHD flow with Coriolis force are obtained. In this paper, we study the fitness problem of weak solutions of MHD equations in bounded domain. By using Galerkin method and a priori estimate, we prove the existence and uniqueness of weak solution (u (., t), B (., t) 鈭，
本文编号：2293024
[Abstract]:Based on the Euler equation and considering the viscosity of the fluid, the Navier-Stokes equation can be proposed in this paper. When the magnetic field is studied, the magnetohydrodynamic, equation is proposed. The MHD model is widely used in many fields such as geophysics, astronomy, engineering and so on. It is one of the simplest models to describe the interaction between conductive fluid and magnetic field. In this paper, the motion of an ideal incompressible MHD flow with Coriolis force in an infinite rotating cylinder is considered, and the stability and instability criteria of the stationary solution of the MHD flow with Coriolis force are obtained. In this paper, we study the fitness problem of weak solutions of MHD equations in bounded domain. By using Galerkin method and a priori estimate, we prove the existence and uniqueness of weak solution (u (., t), B (., t) 鈭，
本文编号：2293024
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