Formation of Shocks for 2D Isentropic Compressible Euler
Formation of Shocks for 2D Isentropic Compressible Euler
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DOI：
10.1002/cpa.21956
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发表时间：
2019-07
影响因子：
3
通讯作者：
T. Buckmaster;S. Shkoller;V. Vicol
中科院分区：
文献类型：
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作者：
T. Buckmaster;S. Shkoller;V. Vicol
考虑二维等熵可压缩Euler方程，压力律为p（ρ）=（1γ）ργ，其中γ > 1.我们提供了一个基本的建设性的证明激波形成从光滑的初始数据的有限能量，没有真空区，并与非平凡的涡。我们证明了对于具有最小斜率−1ε的初始数据，当ε > 0相对于O1振幅足够小时，存在形成时间为Oε的激波的欧拉方程的光滑解。爆破时间和位置可以显式计算，爆破时的解是尖点型的，具有Hölder C13正则性。
We consider the 2D isentropic compressible Euler equations, with pressure law p(ρ) = (1γ)ργ, with γ > 1. We provide an elementary constructive proof of shock formation from smooth initial data of finite energy, with no vacuum regions, and with nontrivial vorticity. We prove that for initial data which has minimum slope −1ε, for ε > 0 taken sufficiently small relative to the O1 amplitude, there exist smooth solutions to the Euler equations which form a shock in time Oε . The blowup time and location can be explicitly computed and solutions at the blowup time are of cusp‐type, with Hölder C13 regularity.