Two-Dimensional Steady Supersonic Exothermically Reacting Euler Flow past Lipschitz Bending Walls

摘要

We are concerned with the two-dimensional steady supersonic reacting Eulerflow past Lipschitz bending walls that are small perturbations of a convex one,and establish the existence of global entropy solutions when the totalvariation of both the initial data and the slope of the boundary issufficiently small. The flow is governed by an ideal polytropic gas andundergoes a one-step exothermic chemical reaction under the reaction ratefunction that is Lipschtiz and has a positive lower bound. The heat released bythe reaction may cause the total variation of the solution to increase alongthe flow direction. We employ the modified wave-front tracking scheme toconstruct approximate solutions and develop a Glimm-type functional byincorporating the approximate strong rarefaction waves and Lipschitz bendingwalls to obtain the uniform bound on the total variation of the approximatesolutions. Then we employ this bound to prove the convergence of theapproximate solutions to a global entropy solution that contains a strongrarefaction wave generated by the Lipschitz bending wall. In addition, theasymptotic behavior of the entropy solution in the flow direction is alsoanalyzed.