Well-posedness of the Euler equation in Triebel–Lizorkin–Morrey spaces

Abstract

ABSTRACTThis 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 . 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.