High concentration property on discontinuity in two-dimensional unsteady compressible Euler equations

We propose a new definition of measure-valued solutions for the two dimensional Euler equations with general pressure laws. This generalization of the traditional weak solutions can describe flow fields with properties of high concentrations on mass and momentum. We derive the intrinsic partial differential equations governing the front surface of the concentration discontinuities, which can at certain extend be considered as generalization of the classical Rankine-Hugoniot conditions for the Euler equations.

We also get some new application results to singular Riemann problems of pressureless Euler equations.