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- W4318145976 abstract "The aim of this note is to present the recent results in [Buckmaster, Cao-Labora, G'omez-Serrano, 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, Raphael, Rodnianski, and Szeftel [Merle, Raphael, Rodnianski, and Szeftel, Ann. of Math., 196(2):567-778, 2022, Ann. of Math., 196(2):779-889, 2022, Invent. Math., 227(1):247-413, 2022] and proves the existence of self-similar profiles for all adiabatic exponents $gamma>1$ in the case of Euler; as well as proving asymptotic self-similar blow-up for $gamma=frac75$ 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." @default.
- W4318145976 created "2023-01-26" @default.
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- W4318145976 date "2023-01-24" @default.
- W4318145976 modified "2023-09-26" @default.
- W4318145976 title "Smooth self-similar imploding profiles to 3D compressible Euler" @default.
- W4318145976 doi "https://doi.org/10.48550/arxiv.2301.10101" @default.
- W4318145976 hasPublicationYear "2023" @default.
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