The Cauchy problem of plasma equations modelling magnetic-curvature-driven Rayleigh-Taylor instability in 3D. (English) Zbl 1474.35232

Summary: Recently, S. Kondo and A. Tani in [SIAM J. Math. Anal. 43, No. 2, 925–943 (2011; Zbl 1225.35228)] 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.


35G50 Systems of nonlinear higher-order PDEs
35G55 Initial value problems for systems of nonlinear higher-order PDEs
35K46 Initial value problems for higher-order parabolic systems


Zbl 1225.35228