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arXiv · 2410.05599

Instability of Data-to-Solution Map for the Log-Regularized 2D Euler System

Xuan-Truong Vu
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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 $\gamma \ge 0$. Furthermore, we show that for $\gamma$ close to $0$, the data-to-solution map is not uniformly continuous in the Sobolev $H^s(\mathbb{R}^2)$ topology for any $s>2$.

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Xuan-Truong Vu. 2024-10-08. Instability of Data-to-Solution Map for the Log-Regularized 2D Euler System. https://arxiv.org/abs/2410.05599

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