Analyticity estimates for the 3D magnetohydrodynamic equations

Abstract

This paper was concerned with the Cauchy problem of the 3D magnetohydrodynamic (MHD) system. We first proved that this system was local well-posed with initial data in the Besov space $ \dot{B}^{s}_{p, q}(\mathbb{R}^{3}) $, in the critical Besov space $ \dot{B}^{-1+\frac{3}{p}}_{p, q}(\mathbb{R}^{3}) $, and in $ L^{p}(\mathbb{R}^{3}) $ with $ p\in]3, 6[ $, respectively. We also obtained a new growth rate estimates for the analyticity radius.

Keywords

• magnetohydrodynamic equations
• the analyticity radius
• besov spaces
• gevrey regularity
• global solution