On the inviscid limit of the 2D Navier-Stokes equations with vorticity belonging to BMO-type spaces

Frederic Bernicot; Tarek Elgindi; Sahbi Keraani

doi:10.1016/j.anihpc.2014.12.001

On the inviscid limit of the 2D Navier-Stokes equations with vorticity belonging to BMO-type spaces

Frederic Bernicot, Tarek Elgindi, Sahbi Keraani

Mathematics

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

6 Scopus citations

Abstract

In a recent paper [6], the global well-posedness of the two-dimensional Euler equation with vorticity in L¹ ∩ LBMOwas proved, where LBMOis a Banach space which is strictly imbricated between L^∞ and BMO. In the present paper we prove a global result on the inviscid limit of the Navier.Stokes system with data in this space and other spaces with the same BMO flavor. Some results of local uniform estimates on solutions of the Navier.Stokes equations, independent of the viscosity, are also obtained.

Original language	English (US)
Pages (from-to)	597-619
Number of pages	23
Journal	Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire
Volume	33
Issue number	2
DOIs	https://doi.org/10.1016/j.anihpc.2014.12.001
State	Published - Mar 1 2016

All Science Journal Classification (ASJC) codes

Analysis
Mathematical Physics
Applied Mathematics

Keywords

2D incompressible Navier-Stokes equations
BMO-type space
Global well-posedness
Inviscid limit

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10.1016/j.anihpc.2014.12.001

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abstract = "In a recent paper [6], the global well-posedness of the two-dimensional Euler equation with vorticity in L1 ∩ LBMOwas proved, where LBMOis a Banach space which is strictly imbricated between L∞ and BMO. In the present paper we prove a global result on the inviscid limit of the Navier.Stokes system with data in this space and other spaces with the same BMO flavor. Some results of local uniform estimates on solutions of the Navier.Stokes equations, independent of the viscosity, are also obtained.",

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T1 - On the inviscid limit of the 2D Navier-Stokes equations with vorticity belonging to BMO-type spaces

AU - Bernicot, Frederic

AU - Elgindi, Tarek

AU - Keraani, Sahbi

PY - 2016/3/1

Y1 - 2016/3/1

N2 - In a recent paper [6], the global well-posedness of the two-dimensional Euler equation with vorticity in L1 ∩ LBMOwas proved, where LBMOis a Banach space which is strictly imbricated between L∞ and BMO. In the present paper we prove a global result on the inviscid limit of the Navier.Stokes system with data in this space and other spaces with the same BMO flavor. Some results of local uniform estimates on solutions of the Navier.Stokes equations, independent of the viscosity, are also obtained.

AB - In a recent paper [6], the global well-posedness of the two-dimensional Euler equation with vorticity in L1 ∩ LBMOwas proved, where LBMOis a Banach space which is strictly imbricated between L∞ and BMO. In the present paper we prove a global result on the inviscid limit of the Navier.Stokes system with data in this space and other spaces with the same BMO flavor. Some results of local uniform estimates on solutions of the Navier.Stokes equations, independent of the viscosity, are also obtained.

KW - 2D incompressible Navier-Stokes equations

KW - BMO-type space

KW - Global well-posedness

KW - Inviscid limit

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On the inviscid limit of the 2D Navier-Stokes equations with vorticity belonging to BMO-type spaces

Abstract

All Science Journal Classification (ASJC) codes

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