Vorticity existence of an ideal incompressible fluid in $B^0_{\infty , 1} (\mathbb{R}^3) \cap L^p(\mathbb{R}^3)$

Abstract

We prove a local (in time) unique vorticity existence for the Euler equation of an ideal incompressible fluid in a critical Besov space $\mathbf{B}_{\infty , 1}^{0}(\mathbb{R}^3) \cap \mathbf{L}^{p}(\mathbb{R}^3)$ with the initial vorticity $\omega _{0} \in \mathbf{B}_{\infty , 1}^{0}(\mathbb{R}^3) \cap \mathbf{L}^{p}(\mathbb{R}^3)$ for some $1 < p < 3$.