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| Shock Formation for 2D Isentropic Euler Equations with Self-similar Variables |
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Citation： |
Wenze SU.Shock Formation for 2D Isentropic Euler Equations with Self-similar Variables[J].Chinese Annals of Mathematics B,2024,45(3):349~412 |
| Page view： 1097
Net amount： 683 |
Authors： |
Wenze SU; |
Foundation： |
the China Scholarship Council (No. 202106100096). |
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| 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-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. 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. |
Keywords： |
2D isentropic Euler equations, Shock formation, Self-similar solution |
Classification： |
35Q31, 35L67, 35B44 |
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