Study On Two - Dimensional Euler Reaction Flow Equations

In this dissertation, we study the two-dimentional steady reacting Euler flow system, including the existence of global entropy solutions for the half-space problem and the existence and asymptotic behavior of reacting supersonic flow passing a Lipchitz wedge with small incident angle.Firstly, we consider the half-space problem. When the incoming flow is super-sonic and the total variation of the initial data is suitably small, we establish the global existence of entropy solution by using fractional Glimm scheme.Secondly, we consider the problem of the reacting Euler flow passing a Lipschitz wedge, where the incident angle is suitably small and so there will be only weak waves emerged. If we treat the x-axis as the time direction, we can formulate the above case as an initial-boundary value problem of quasi-linear hyperbolic systems. When the total variation of the tangent angle functions along the wedge boundary and the total variation of the initial data function are suitably small, we establish the global existence and asymptotic behavior of entropy solutions for this initial-boundary value problem.