The Morawetz problem for supersonic flow with cavitation

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• Simon Schulz (Pisa)
• Monday 26 February 2024, 15:00-16:00
• MR13.

If you have a question about this talk, please contact Dr Greg Taujanskas.

We are concerned with the existence and compactness of entropy solutions of the compressible Euler system for two-dimensional steady potential flow around an obstacle for a polytropic gas with supersonic far-field velocity. The existence problem, initially posed by Morawetz in 1985, has remained open since then. In this work, we establish the first complete existence theorem for the Morawetz problem by developing a new entropy analysis, coupled with a vanishing viscosity method and compensated compactness ideas. The main challenge arises when the flow approaches cavitation, leading to a loss of strict hyperbolicity of the system and a singularity of the entropy equation. This is joint work with Gui-Qiang Chen and Tristan Giron.

This talk is part of the Partial Differential Equations seminar series.

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