Year: 2024
Type: preprint
Abstract: In this paper, we study the logarithmically regularized $2$D Euler system \eqref{e1}, which is derived by regularizing the Euler equation for the vorticity. We establish local well-posedness of the logarithmically regularized $2$D Euler equations in the subcritical space $H^s(\mathbb{R}^2)$ with $s>2$ for $γ\ge 0$. Furthermore, we show that for $γ$ close to $0$, the data-to-solution map is not uniformly continuous in the Sobolev $H^s(\mathbb{R}^2)$ topology for any $s>2$.
Source: arXiv (Cornell University)
Author: Vu, Xuan-Truong
Institution: University of Illinois Chicago
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4403346593