Temporal regularity of the solution to the incompressible Euler equations in the end-point critical Triebel-Lizorkin space $F^{d+1}_{1, \infty}(\mathbb{R}^d)$

Hee Chul Pak

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arXiv · 2303.00487

Temporal regularity of the solution to the incompressible Euler equations in the end-point critical Triebel-Lizorkin space $F^{d+1}_{1, \infty}(\mathbb{R}^d)$

Hee Chul Pak

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Abstract

An evidence of temporal dis-continuity of the solution in $F^s_{1, \infty}(\mathbb{R}^d)$ is presented, which implies the ill-posedness of the Cauchy problem for the Euler equations. Continuity and weak-type continuity of the solutions in related spaces are also discussed.

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Hee Chul Pak. 2023-03-01. Temporal regularity of the solution to the incompressible Euler equations in the end-point critical Triebel-Lizorkin space $F^{d+1}_{1, \infty}(\mathbb{R}^d)$. https://arxiv.org/abs/2303.00487

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