$\mathbb{T}^3$ 与 $\mathbb{R}^3$ 中可压缩Euler与Navier-Stokes方程的非径向内爆
偏微分方程分析
2025-04-22 v2 数学物理
math.MP
摘要
本文构造了可压缩Euler和Navier-Stokes方程的光滑、非径向解，其发展出内爆有限时间奇点。我们的构造受文献[Merle, Raphaël, Rodnianski, and Szeftel, Ann. of Math., 196(2):567-778, 2022, Ann. of Math., 196(2):779-889, 2022]、[Buckmaster, Cao-Labora, and Gómez-Serrano, arXiv:2208.09445, 2022]的启发，但足够灵活以处理周期与非径向初始数据。
引用
@article{arxiv.2310.05325,
title = {Non-radial implosion for compressible Euler and Navier-Stokes in $\mathbb{T}^3$ and $\mathbb{R}^3$},
author = {Gonzalo Cao-Labora and Javier Gómez-Serrano and Jia Shi and Gigliola Staffilani},
journal= {arXiv preprint arXiv:2310.05325},
year = {2025}
}
备注
80 pages, 6 figures. To appear in Cambridge Journal of Mathematics