The Riemann problem for the two-dimensional zero-pressure Euler equations
The author considers the two-dimensional compressible Euler system with zero pressure and energy transport. The domain is \(\mathbb{R}^2\). Total energy consists of the internal energy, changed only by transport, and the kinetic energy of the motion. The initial data are Riemann, constant in each quadrant. An additional assumption is that each initial discontinuity gives only one wave. Twenty three exact solutions are obtained and analyzed. \(\delta\)-shock solutions for both density and energy are revealed. Rankine-Hugoniot relation and entropy condition are proposed.
scientific article; zbMATH DE number 7027391
scientific article