Seunghoon Bang and Yuxi Zheng

Department of Mathematics

Penn State University

The pressure-gradient system is a relatively new system of conservation laws. This system is a reduction from the two-dimensional(2-D) compressible Euler equations. Since the Cauchy problem for these systems is still very difficult, we consider the Riemann problem, but it is also a complex open problem. According to the initial data, we have 12 configurations that explain the interaction between various waves such as rarefaction waves, shocks and contact discontinuities. We proved the existence of solution in one configuration, three rarefaction waves. n an infinite-dimensional semi-group of volume-preserving maps.