Remarks on the Well-Posedness of the Euler Equations in the Triebel–Lizorkin Spaces

Zihua Guo; Kuijie Li

doi:10.1007/s00041-021-09837-y

Remarks on the Well-Posedness of the Euler Equations in the Triebel–Lizorkin Spaces

Zihua Guo, Kuijie Li

School of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

3 Citations (Scopus)

Abstract

We prove the continuous dependence of the solution maps for the Euler equations in the (critical) Triebel–Lizorkin spaces, which was not shown in the previous works [6, 7, 9]. The proof relies on the classical Bona–Smith method as [12], where similar result was obtained in critical Besov spaces B∞,11.

Original language	English
Article number	29
Number of pages	24
Journal	Journal of Fourier Analysis and Applications
Volume	27
Issue number	2
DOIs	https://doi.org/10.1007/s00041-021-09837-y
Publication status	Published - Apr 2021

Keywords

Commutator estimates
Continuous dependence
Euler equations

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10.1007/s00041-021-09837-yLicence: CC BY

Cite this

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title = "Remarks on the Well-Posedness of the Euler Equations in the Triebel–Lizorkin Spaces",

abstract = "We prove the continuous dependence of the solution maps for the Euler equations in the (critical) Triebel–Lizorkin spaces, which was not shown in the previous works [6, 7, 9]. The proof relies on the classical Bona–Smith method as [12], where similar result was obtained in critical Besov spaces B∞,11.",

keywords = "Commutator estimates, Continuous dependence, Euler equations",

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AU - Guo, Zihua

AU - Li, Kuijie

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N2 - We prove the continuous dependence of the solution maps for the Euler equations in the (critical) Triebel–Lizorkin spaces, which was not shown in the previous works [6, 7, 9]. The proof relies on the classical Bona–Smith method as [12], where similar result was obtained in critical Besov spaces B∞,11.

AB - We prove the continuous dependence of the solution maps for the Euler equations in the (critical) Triebel–Lizorkin spaces, which was not shown in the previous works [6, 7, 9]. The proof relies on the classical Bona–Smith method as [12], where similar result was obtained in critical Besov spaces B∞,11.

KW - Commutator estimates

KW - Continuous dependence

KW - Euler equations

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Remarks on the Well-Posedness of the Euler Equations in the Triebel–Lizorkin Spaces

Abstract

Keywords

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Harmonic analysis and dispersive partial differential equations

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Remarks on the Well-Posedness of the Euler Equations in the Triebel–Lizorkin Spaces

Abstract

Keywords

Access to Document

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Projects

Harmonic analysis and dispersive partial differential equations

Cite this