Existence and Regularity of Sonic‐Supersonic Solutions for 2‐D Steady Magnetohydrodynamics System With van der Waals Fluid

ABSTRACT This work deals with the existence of a sonic‐supersonic solution near the sonic curve for the 2‐D steady magnetohydrodynamics system with the van der Waals fluid. An idea of characteristic decomposition is used to transform the steady magnetohydrodynamics system into a new system involving the variables and , which shows a clear singularity‐regularity structure. By employing the Banach fixed point theorem, we prove the existence of solution in the ‐plane under certain assumptions on boundary data. An inversion of the solution from ‐plane to the original ‐plane has been discussed. For the regularity of the solution, we have used the partial hodograph transformation and shown that solution has ‐regularity up to the sonic curve.