Supersonic Flow In The Shock Wave Reflection In Lipschitz Continuous Solid Wall

From[1], we know that if the incident angle of the shock front is small, regular reflection would occur when the incident oblique shock impinges on the flat fixed wall. For very weak stationary shocks, the shock lines are approximately Mach lines and form Mach angles with the wall, therefore the stationary flow patten containing a weak "incident" and "reflected" shock agrees with the law of reflection of geometrical optics, i.e., both shock lines form the same angle with the wall. When the incident or reflected shock has appreciable strength but the incident angle still is less than the extreme angle determined by the shock polar of the oncoming flow, regular reflection would also occur but the angles between incident and reflected waves with the wall are in general not equal. This dissertation studies the case when the wall is Lipschitz continuous, that is, we study the regular reflection problem of the shock front on an Lipschitz perturbed wall in the steady potential supersonic flow. By a modified Glimm scheme, we obtain the global weak solution, under the hypotheses that each of the vertex angle, i.e., the angle between the oncoming flow velocity and the tangent line of the perturbed wall is less than the extreme angle determined by the shock polar of the oncoming flow, and the total variation of tangent angle along each edge is sufficiently small. In addition, a sequence of the corresponding approximate leading shock fronts is shown to be convergent to the leading incident and reflected shock fronts of the obtained solution.