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The Cauchy problem of plasma equations modelling magnetic-curvature-driven Rayleigh–Taylor instability in 3D
Differential and Integral Equations ( IF 1.4 ) Pub Date : 2020-07-14
Boling Guo, Xinglong Wu

Recently, S. Kondo and A. Tani in SIAM J. Math. Anal. (see [9]) investigated the existence and uniqueness of the strong solution to the initial boundary value problem (IBVP) of electromagnetic fluid equations (1.4) with the magnetic-curvature-driven Rayleigh–Taylor instability on bounded domain in 3D. The present paper will improve and extend the results from bounded domain to $\mathbb{R}^3$. First, we establish the local well-posedness of the Cauchy problem for the equation (1.4) and obtain some important estimates of the solution to the plasma equations in $\mathbb{R}^3$ by some lemmas, thanks to these lemmas, we establish the global solution of the Cauchy problem of the equation. Secondly, the existence of global attractor of the plasma equations in a bounded domain of $\mathbb{R}^3$ is established. Finally, we obtain the Hausdorff and fractal dimensions of the global attractor of the equation.

中文翻译:

等离子体方程的Cauchy问题,用于建模3D的磁曲率驱动的Rayleigh-Taylor不稳定性

最近,SIAM J. Math。中的S. Kondo和A. Tani。肛门 (见[9])研究了电磁流体方程(1.4)的初始边界值问题(IBVP)在3D有界区域上的磁曲率驱动的瑞利-泰勒不稳定性的强解的存在和唯一性。本文将改进并将结果从有界域扩展到$ \ mathbb {R} ^ 3 $。首先,我们为方程(1.4)建立Cauchy问题的局部适定性,并通过一些引理得到$ \ mathbb {R} ^ 3 $中的等离子体方程解的一些重要估计,这要归功于这些引理,我们建立方程柯西问题的整体解。其次,建立了在$ \ mathbb {R} ^ 3 $的有界域中等式的整体吸引子的存在。最后,
更新日期:2020-08-20
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