JournalsaihpcVol. 33, No. 2pp. 597–619

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

  • Frédéric Bernicot

    CNRS – Université de Nantes, Laboratoire de Mathématiques Jean Leray, 2, Rue de la Houssinière, 44322 Nantes Cedex 03, France
  • Tarek Elgindi

    Courant Institute of Mathematical Sciences, 251 Mercer Street, New York, 10012-1185 NY, USA
  • Sahbi Keraani

    UFR de Mathématiques, Université de Lille 1, 59655 Villeneuve d'Ascq Cedex, France
On the inviscid limit of the 2D Navier–Stokes equations with vorticity belonging to BMO-type spaces cover
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Abstract

In a recent paper [6], the global well-posedness of the two-dimensional Euler equation with vorticity in L1LBMOL^{1} \cap \mathrm{LBMO} was proved, where LBMO is a Banach space which is strictly imbricated between LL^{\infty } 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.

Cite this article

Frédéric Bernicot, Tarek Elgindi, Sahbi Keraani, On the inviscid limit of the 2D Navier–Stokes equations with vorticity belonging to BMO-type spaces. Ann. Inst. H. Poincaré Anal. Non Linéaire 33 (2016), no. 2, pp. 597–619

DOI 10.1016/J.ANIHPC.2014.12.001