【摘要】：本文從Euler方程出發(fā),考慮流體粘性可以提出Navier-Stokes方程,當(dāng)研究磁場作用時提出了磁流體力學(xué)(magnetohydrodynamic,簡稱MHD)方程。磁流體力學(xué)系統(tǒng)描述粘性或無粘性,可壓縮或不可壓縮導(dǎo)電流體與磁場間的相互作用。MHD模型在諸如地球物理學(xué),天文學(xué),工程學(xué)等許多領(lǐng)域都有廣泛的應(yīng)用,它是描述導(dǎo)電流體與磁場間相互作用的最簡單的模型之一。本文考慮在無限長旋轉(zhuǎn)圓柱內(nèi)帶有科氏力的理想不可壓縮MHD流的運動,得到了帶有科氏力的MHD流定態(tài)解的穩(wěn)定性和不穩(wěn)定性判據(jù);另外,我們研究有界區(qū)域中MHD方程組弱解的適定性問題,利用Galerkin方法和先驗估計,證明了當(dāng)(u0,B0)∈((Wm,p(Ω))2×Wm,p)(Ω)時,弱解(u(.,t),B(.,t))∈((Wm,p(Ωm,(Ω))2 × 的存在唯一性及其對初值的連續(xù)依賴性;進一步,我們研究了N維有界區(qū)域中理想不可壓縮MHD方程組強解的適定性問題,利用Galerkin方法和先驗估計,證明了當(dāng)(u0,B0)∈((Hm(Ω))N×(Hm(Ω))N)時,強解(u(·,t),B(·,t))∈((Hm Ω))N×(Hm(Ω)N)的存在唯一性及其對初值的連續(xù)依賴性。
[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，

本文編號：2293024