Global classical solution to 3D compressible magnetohydrodynamic equations with large initial data and vacuum

Abstract

In this paper, we study the Cauchy problem of the isentropic compressible magnetohydrodynamic equations in ${\mathbb{R}}^3$. When $(\gamma -1{)}^{\frac{1}{6}}{E}_0^{\frac{1}{2}}$, together with the $\Vert H_0{\Vert }_{L^2}$, is suitably small, a result on the existence of global classical solutions is obtained. It should be pointed out that the initial energy $E_0$ except the $L^2$- norm of $H_0$ can be large as $\gamma$ goes to 1, and that throughout the proof of the theorem in the present paper, we make no restriction upon the initial data $({\rho }_0,u_0)$. Our result improves the one established by Li-Xu-Zhang in \cite{H.L. L}, where, with small initial engergy, the existence of classical solution was proved.

arXiv comment36 pages

References in corpus (4)

• Global Existence and Large-Time Behavior of Solutions to the Three-Dimensional Equations of Compressible Magnetohydrodynamic Flows
• Global solutions to the three-dimensional full compressible magnetohydrodynamic flows
• Incompressible limit of the compressible magnetohydrodynamic equations with vanishing viscosity coefficients
• Global classical solution to 3D isentropic compressible Navier-Stokes equations with large initial data and vacuum