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Applicable Analysis
An International Journal
Volume 99, 2020 - Issue 5
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Articles

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

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Pages 772-795 | Received 09 Mar 2018, Accepted 07 Aug 2018, Published online: 26 Aug 2018
 

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 Fp,q,rs(Rd), d2. 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.

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Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The authors are partially supported by NSF of China [grant numbers 11261023 and 11461033, 11401269], the Natural Science Foundation of Jiangxi Province [grant number 20171BAB201003] and the foundation of CSC [grant number 201609470010] and CSC [grant number 201608360133].

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