Weak limits of solutions to the steady incompressible two-dimensional Euler equation in a bounded domain

Article type: Research Article

Authors: Bethuel, Fabrice | Ghidaglia, Jean-Michel^;

Affiliations: Laboratoire d'Analyse Numérique, Université Paris-Sud, Département de Mathématiques, Bâtiment 425, 91405 Orsay Cedex, France | Centre de Mathématiques et de Leurs Applications, Ecole Normale Supérieure de Cachan et CNRS, 61 Avenue du Président Wilson, 94235 Cachan Cedex, France

Note: [] Correspondence to: J.-M. Ghidaglia, Centre de Mathématiques et de Leurs Applications, Ecole Normale Supérieure de Cachan et CNRS, 61 Avenue du Président Wilson, 94235 Cachan Cedex, France.

Abstract: In this work we show that any sequence uε of smooth solutions to the steady incompressible two-dimensional Euler equation in a bounded domain Ω, which converges weakly in L2(Ω) as ε goes to zero, converges to a weak solution of this equation provided curl uε remains bounded in L1(Ω).

DOI: 10.3233/ASY-1994-8305

Journal: Asymptotic Analysis, vol. 8, no. 3, pp. 277-291, 1994