## Differential and Integral Equations

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

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

#### 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