Differential and Integral Equations

The Cauchy problem of plasma equations modelling magnetic-curvature-driven Rayleigh–Taylor instability in 3D

Boling Guo and Xinglong Wu

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

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.

Article information

Source
Differential Integral Equations, Volume 33, Number 7/8 (2020), 361-392.

Dates
First available in Project Euclid: 14 July 2020

Permanent link to this document
https://projecteuclid.org/euclid.die/1594692054

Mathematical Reviews number (MathSciNet)
MR4122510

Subjects
Primary: 35G50: Nonlinear higher-order systems 35G55: Initial value problems for nonlinear higher-order systems 35K46: Initial value problems for higher-order parabolic systems

Citation

Guo, Boling; Wu, Xinglong. The Cauchy problem of plasma equations modelling magnetic-curvature-driven Rayleigh–Taylor instability in 3D. Differential Integral Equations 33 (2020), no. 7/8, 361--392. https://projecteuclid.org/euclid.die/1594692054


Export citation