Smooth self-similar imploding profiles to 3D compressible Euler
Smooth self-similar imploding profiles to 3D compressible Euler
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DOI：
10.1090/qam/1661
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发表时间：
2023-01
影响因子：
0.8
通讯作者：
T. Buckmaster;Gonzalo Cao-Labora;Javier G'omez-Serrano
中科院分区：
文献类型：
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作者：
T. Buckmaster;Gonzalo Cao-Labora;Javier G'omez-Serrano
本说明的目的是介绍Buckmaster，Cao-Labora和Gómez-Serrano的最新结果[平滑暗示了3D可压缩流体的解决方案，Arxiv Preprint Arxiv：2208.09445，2022]，涉及“触发3D的3D”的存在等等的Euler和Navier-Stokes方程（2022），第247-413页。在Euler的情况下，所有绝热指数γ> 1 \ 1 \ gamma> 1的自相似轮廓的存在； Navier-Stokes。解决方案的密度远离零和恒定，这是在这种设置中的第一个爆炸示例。
The aim of this note is to present the recent results by Buckmaster, Cao-Labora, and Gómez-Serrano [Smooth imploding solutions for 3D compressible fluids, Arxiv preprint arXiv:2208.09445, 2022] concerning the existence of “imploding singularities” for the 3D isentropic compressible Euler and Navier-Stokes equations. Our work builds upon the pioneering work of Merle, Raphaël, Rodnianski and Szeftel [Invent. Math. 227 (2022), pp. 247–413; Ann. of Math. (2) 196 (2022), pp. 567–778; Ann. of Math. (2) 196 (2022), pp. 779–889] and proves the existence of self-similar profiles for all adiabatic exponents γ > 1 \gamma >1 in the case of Euler; as well as proving asymptotic self-similar blow-up for γ = 7 5 \gamma =\frac 75 in the case of Navier-Stokes. Importantly, for the Navier-Stokes equation, the solution is constructed to have density bounded away from zero and constant at infinity, the first example of blow-up in such a setting. For simplicity, we will focus our exposition on the compressible Euler equations.