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July/August 2020 The Cauchy problem of plasma equations modelling magnetic-curvature-driven Rayleigh–Taylor instability in 3D
Boling Guo, Xinglong Wu
Differential Integral Equations 33(7/8): 361-392 (July/August 2020).

Abstract

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.

Citation

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Boling Guo. Xinglong Wu. "The Cauchy problem of plasma equations modelling magnetic-curvature-driven Rayleigh–Taylor instability in 3D." Differential Integral Equations 33 (7/8) 361 - 392, July/August 2020.

Information

Published: July/August 2020
First available in Project Euclid: 14 July 2020

zbMATH: 07250699
MathSciNet: MR4122510

Subjects:
Primary: 35G50, 35G55, 35K46

Rights: Copyright © 2020 Khayyam Publishing, Inc.

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Vol.33 • No. 7/8 • July/August 2020
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