Well-posedness of the Euler equation in Triebel–Lizorkin–Morrey spaces. Issue 5 (3rd April 2020) - Chen, Dongxiang; Chen, Xiaoli; Sun, Lijing
ABSTRACT: This paper establishes the local existence, uniqueness and a blow-up criterion for the solutions to the inviscid incompressible Euler equation in Triebel–Lizorkin–Morrey space F p, q, r s ( R d ), d ≥ 2 . As an application, we also derive the global persistence of the initial regularity in Triebel–Lizorkin–Morrey space for the solutions of 2-D Euler equation. These results are established using the logarithmic inequality of Beal–Kato–Majda type, the Moser type of inequality and commutator estimates in Triebel–Lizorkin–Morrey space.