二维粘性系数依赖于密度的不可压MHD方程组强解的全局存在性

发布时间：2018-06-18 23:54

  本文选题：不可压缩流 + 非齐次MHD方程组　； 参考：《西北大学》2017年硕士论文

【摘要】：本文主要研究了粘性系数μ(ρ)与磁扩散系数v(ρ)都依赖于密度ρ时,2维不可压缩磁流体方程组在有界区域内强解的全局存在性.方程的主要形式为(?)初始条件(ρ，u,B)|t=0=(ρ0,u0,B0),在Ω内.边界条件u=0,B·(?)=0,curlB=0,d(?)Ω×[0,T)内.其中Ω(?)R2.变量ρ(x,t),u(x,t)分别代表流体的密度与速度;B(x,t)为磁场;P(x,t)为压力.μ(ρ),υ(ρ)分别表示粘性系数和磁扩散系数均依赖于密度ρ,并且满足μ(ρ),υ(ρ)∈ C1[0,∞),0＜μ≤μ≤(?)和v≤v≤(?) 当ρ∈[0,∞)时.其中(?)为正常数.
[Abstract]:In this paper, we study the global existence of strong solutions for incompressible magnetohydrodynamic equations in a bounded region when both viscosity coefficient 渭 (蟻) and magnetic diffusion coefficient v (蟻) depend on density 蟻. The main form of the equation is The initial condition (蟻 ~ (U) B) (蟻 _ (0) U _ (0) B _ (0) is in 惟. The boundary conditions are in the 惟 脳 [0T]. Among them, omega R2. The variable 蟻 ~ (x) (v (v) represents the density and velocity of the fluid, respectively) and the velocity of the fluid is a magnetic field. (渭 (蟻, v (蟻) respectively denotes that the viscosity coefficient and the magnetic diffusion coefficient depend on the density 蟻, and satisfy 渭 (蟻, v (蟻) 鈭，

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