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- Title
Shock Formation for 2D Isentropic Euler Equations with Self-similar Variables.
- Authors
Su, Wenze
- Abstract
The author studies the 2D isentropic Euler equations with the ideal gas law. He exhibits a set of smooth initial data that give rise to shock formation at a single point near the planar symmetry. These solutions to the 2D isentropic Euler equations are associated with non-zero vorticity at the shock and have uniform-in-time 1 3 -Hölder 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. The proof of the solutions, following the 3D construction of Buckmaster, Shkoller and Vicol (in 2023), is based on the stable 2D self-similar Burgers profile and the modulation method.
- Subjects
IDEAL gases; STATISTICAL smoothing; VORTEX motion; EULER equations; BURGERS' equation
- Publication
Chinese Annals of Mathematics, 2024, Vol 45, Issue 3, p349
- ISSN
0252-9599
- Publication type
Article
- DOI
10.1007/s11401-024-0020-x