Well-posedness of the Euler equation in Triebel–Lizorkin–Morrey spaces. Issue 5 (3rd April 2020)

• Record Type: Journal Article
• Authors: Chen, Dongxiang; Chen, Xiaoli; Sun, Lijing
• Is Part Of: Applicable analysis. Volume 99:Issue 5(2020)
• Page Start: 772
• Page End: 795
• Publication Date: 2020-04-03
• Subjects: Ming Mei; Euler equation -- Triebel–Lizorkin–Morrey space -- local well-posedness -- blow-up criterion -- paraproduct; Primary: 35Q35 -- Secondary: 76B03 -- 35E15; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2018.1510491
• Languages: English
• ISSNs: 0003-6811

Abstract

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.