Global weak solutions of the equations of compressible

Anthony SuenUSC

We prove the global-in-time existence of weak solutions of the three-dimensional isothermal, compressible magnetohydrodynamic (MHD) equations in the whole R^3 space. The initial density is strictly positive, essentially bounded and is close to a constant in L^2, and the initial velocity and magnetic field are both small in L^2 and bounded in L^n for some n>6. Here the initial data may be discontinuous across a hypersurface of R^3.