Global Low-Energy Weak Solutions of the Equations of Three-Dimensional Compressible Magnetohydrodynamics

• DOI: 10.1007/s00205-012-0498-3
• Publication Date: 2012-02-17T09:16:26Z
• Authors: Anthony Suen; David Hoff
• Keywords: Compressible flow; Divergence (linguistics)

We prove the global-in-time existence of weak solutions of the equations of compressible magnetohydrodynamics in three space dimensions with initial data small in L2 and initial density positive and essentially bounded. A great deal of information concerning partial regularity is obtained: velocity, vorticity, and magnetic field become relatively smooth in positive time (H1 but not H2) and singularities in the pressure cancel those in a certain multiple of the divergence of the velocity, thus giving concrete expression to conclusions obtained formally from the Rankine–Hugoniot conditions.