On the global well-posedness for Euler equations with unbounded vorticity

Frédéric Bernicot; Taoufik Hmidi

doi:10.4310/DPDE.2015.v12.n2.a3

On the global well-posedness for Euler equations with unbounded vorticity

Frédéric Bernicot, Taoufik Hmidi

Mathematics

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

Abstract

In this paper, we are interested in the global persistence regularity for the 2D incompressible Euler equations in some function spaces allowing unbounded vorticities. More precisely, we prove the global propagation of the vorticity in some weighted Morrey-Campanato spaces and in this framework the velocity field is not necessarily Lipschitz but belongs to the log-Lipschitz class L^αL, for some α ∈ (0,1).

Original language	English (US)
Pages (from-to)	127-155
Number of pages	29
Journal	Dynamics of Partial Differential Equations
Volume	12
Issue number	2
DOIs	https://doi.org/10.4310/DPDE.2015.v12.n2.a3
State	Published - Jun 27 2015

Keywords

2D incompressible Euler equations
BMOtype space
Global well-posedness

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.4310/DPDE.2015.v12.n2.a3

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abstract = "In this paper, we are interested in the global persistence regularity for the 2D incompressible Euler equations in some function spaces allowing unbounded vorticities. More precisely, we prove the global propagation of the vorticity in some weighted Morrey-Campanato spaces and in this framework the velocity field is not necessarily Lipschitz but belongs to the log-Lipschitz class LαL, for some α ∈ (0,1).",

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N2 - In this paper, we are interested in the global persistence regularity for the 2D incompressible Euler equations in some function spaces allowing unbounded vorticities. More precisely, we prove the global propagation of the vorticity in some weighted Morrey-Campanato spaces and in this framework the velocity field is not necessarily Lipschitz but belongs to the log-Lipschitz class LαL, for some α ∈ (0,1).

AB - In this paper, we are interested in the global persistence regularity for the 2D incompressible Euler equations in some function spaces allowing unbounded vorticities. More precisely, we prove the global propagation of the vorticity in some weighted Morrey-Campanato spaces and in this framework the velocity field is not necessarily Lipschitz but belongs to the log-Lipschitz class LαL, for some α ∈ (0,1).

KW - 2D incompressible Euler equations

KW - BMOtype space

KW - Global well-posedness

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On the global well-posedness for Euler equations with unbounded vorticity

Abstract

Keywords

ASJC Scopus subject areas

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