A new type of stable shock formation in gas dynamics

IF 1 3区 数学 Q1 MATHEMATICS
Isaac Neal, Calum Rickard, Steve Shkoller, Vlad Vicol
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引用次数: 0

Abstract

From an open set of initial data, we construct a family of classical solutions to the 1D nonisentropic compressible Euler equations which form $ C^{0,\nu} $ cusps as a first singularity, for any $ \nu \in [\frac{1}{2}, 1) $. For this range of $ \nu $, this is the first result demonstrating the stable formation of such $ C^{0,\nu} $ cusp-type singularities, also known as pre-shocks. The proof uses a new formulation of the differentiated Euler equations along the fast acoustic characteristic, and relies on a novel set of $ L^p $ energy estimates for all $ 1
气体动力学中一种新型稳定激波形成
从一个开放的初始数据集,我们构造了一维非等熵可压缩欧拉方程的经典解族,这些方程形成$ C^{0,\nu} $顶点作为第一奇点,对于任何$ \nu \in [\frac{1}{2}, 1) $。对于这个$ \nu $范围,这是第一个证明这种$ C^{0,\nu} $尖型奇点(也称为预冲击)稳定形成的结果。该证明使用了沿快速声学特性的微分欧拉方程的新公式,并依赖于所有$ 1<p<\infty $的一组新的$ L^p $能量估计,这可能是独立的兴趣。
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来源期刊
CiteScore
1.90
自引率
10.00%
发文量
124
审稿时长
4-8 weeks
期刊介绍: CPAA publishes original research papers of the highest quality in all the major areas of analysis and its applications, with a central theme on theoretical and numeric differential equations. Invited expository articles are also published from time to time. It is edited by a group of energetic leaders to guarantee the journal''s highest standard and closest link to the scientific communities.
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