Three-dimensional interaction of shocks in irrotational flows
Confluentes Mathematici, Volume 3 (2011) no. 3, pp. 543-576.

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.

Published online:
DOI: 10.1142/S1793744211000394
Denis Serre 1

1
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Denis Serre. Three-dimensional interaction of shocks in irrotational flows. Confluentes Mathematici, Volume 3 (2011) no. 3, pp. 543-576. doi : 10.1142/S1793744211000394. https://cml.centre-mersenne.org/articles/10.1142/S1793744211000394/

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