Local well-posedness and low Mach number limit of the compressible magnetohydrodynamic equations in critical spaces

The local well-posedness and low Mach number limit are considered for the multi-dimensional isentropic compressible viscous magnetohydrodynamic equations in critical spaces. First the local well-posedness of solution to the viscous magnetohydrodynamic equations with large initial data is established. Then the low Mach number limit is studied for general large data and it is proved that the solution of the compressible magnetohydrodynamic equations converges to that of the incompressible magnetohydrodynamic equations as the Mach number tends to zero. Moreover, the convergence rates are obtained.Comment: 37page

A Foreword from the Editor-in-Chief

Accompanying the development of petrochemical industry, great progress has been achieved in the organic polymer materials. It is well known that the conventional polymer materials usually consist of organosilicon polymers, polycarbonates, polyethylene, polyamide, polyurethane, polysulfone, phenolic resin and so on. Although their synthesis and applications have been well developed, the further research on them still has great significance. Moreover, natural polymers such as polysaccharides, tannins, cellulose also occupy an important position in the family of the organic polymer materials