THREE-DIMENSIONAL INTERACTION OF SHOCKS IN IRROTATIONAL FLOWS

Confluentes Mathematici

SERRE, DENIS¹ 

[1] UMPA, UMR CNRS–ENS Lyon # 5669, École Normale Supérieure de Lyon 46, allée d'Italie 69364 Lyon, cedex 07, France

关键词: Shock waves;    elliptic PDE;    characteristic boundary-value problem;   

DOI  :  10.1142/S1793744211000394

学科分类：数学（综合）

来源: World Scientific Publishing Co. Pte. Ltd.

【 摘 要 】

The general d-dimensional Riemann problem raises naturally the question of resolving the interaction of d planar shocks merging at a point. In gas dynamics, we may consider only standing shocks. This problem has received a satisfactory answer in dimension d = 2 (see [3, 4]). We investigate the 3-dimensional case. We restrict to the irrotational case, in order to keep the complexity of the solution within reasonable bounds. We show that a new kind of waves appears downstream, which we call a conical wave. When the equation of state is that of Chaplygin/von Kármán, we give a complete mathematical answer to this problem. This involves the existence and uniqueness of a complete minimal surface in a hyperbolic space, with prescribed asymptotics.

【 授权许可】

Unknown