The authors construct smooth characteristic initial data on any admissible cone for the 3D compressible Euler equations, resolving the open characteristic initial data problem.
Shock Interaction in Plane Symmetry
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abstract
We consider the problem of interaction of two oncoming shocks in plane symmetry for a barotropic fluid. We establish a local in time solution after the point of interaction, thereby determining the state behind the emerged shocks which originate at the interaction point. The location of these shocks in space time being unknown the problem constitutes a double free boundary problem, i.e.~complete data for the problem is only given in a single point, the interaction point. This article can be viewed as an extension of the article arXiv:2112.15266 which deals with the reflection of a shock on a wall.
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Constructing characteristic initial data for three dimensional compressible Euler equations
The authors construct smooth characteristic initial data on any admissible cone for the 3D compressible Euler equations, resolving the open characteristic initial data problem.