Stable shock formation for solutions to the multidimensional compressible Euler equations in the presence of non-zero vorticity

Stable shock formation for solutions to the multidimensional compressible Euler equations in the presence of non-zero vorticity

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Jonathan Luk , Stanford University
Fine Hall 314

It is well-known since the foundational work of Riemann that plane symmetric solutions to the compressible Euler equations may form shocks in finite time. For a class of simple plane symmetric solutions, we prove that the phenomenon of shock-formation is stable under perturbations of the initial data that break the plane symmetry with potentially non-vanishing vorticity. In particular, this is the first constructive shock-formation result for which the vorticity is allowed to be non-vanishing at the shock. We show that the vorticity remains bounded all the way up to the shock, and that the dynamics are well-described by the irrotational compressible Euler equations. This is a joint work with J. Speck (MIT), which is partly an extension of an earlier joint work with J. Speck (MIT), G. Holzegel (Imperial) and W. Wong (Michigan State).