Shock Formation for 2D Isentropic Euler Equations with Self-similar Variables  

作　　者：Wenze SU 

机构地区：[1]School of Mathematical Sciences,Fudan University,Shanghai 200433,China

出　　处：《Chinese Annals of Mathematics,Series B》2024年第3期349-412,共64页数学年刊（B辑英文版）

基　　金：supported by the China Scholarship Council(No.202106100096).

摘　　要：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-Holder 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.

关 键 词：2D isentropic Euler equations Shock formation Self-similar solution 

分 类 号：O175[理学—数学]