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

2024/10/08 by Vu, Xuan-Truong
#35B30 #35Q31 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2410.05599

Abstract

In this paper, we study the logarithmically regularized 2D Euler system \eqrefe1, which is derived by regularizing the Euler equation for the vorticity. We establish local well-posedness of the logarithmically regularized 2D Euler equations in the subcritical space H^s(ℝ²) with s>2 for γ≥ 0. Furthermore, we show that for γ close to 0, the data-to-solution map is not uniformly continuous in the Sobolev H^s(ℝ²) topology for any s>2.

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