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arXiv · 2302.14317

Shock formation for 2D Isentropic Euler equations with self-similar variables

Wenze Su
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Abstract

We study the 2D isentropic Euler equations with the ideal gas law. We exhibit a set of smooth initial data that give rise to shock formation at a single point near the planar symmetry. These solutions are associated with non-zero vorticity at the shock and have uniform-in-time 1/3-H\"older bound. Moreover, these point shocks are of self-similar type and share the same profile, which is a solution to the 2D self-similar Burgers equation. Our proof, following the 3D shock formation result of Buckmaster, Shkoller and Vicol, is based on the stable 2D self-similar Burgers profile and the modulation method.

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Wenze Su. 2023-02-28. Shock formation for 2D Isentropic Euler equations with self-similar variables. https://arxiv.org/abs/2302.14317

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