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.
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