caa a22 4500 60551593X CHVBK 20210128105158.0 cr unu---uuuuu 210128e20151201xx s 000 0 eng 10.1007/s00205-015-0889-3 doi (NATIONALLICENCE)springer-10.1007/s00205-015-0889-3 The Two Dimensional Euler Equations on Singular Exterior Domains [Elektronische Daten] [David Gérard-Varet, Christophe Lacave] This paper is a follow-up of Gérard-Varet and Lacave (Arch Ration Mech Anal 209(1):131-170, 2013), on the existence of global weak solutions to the two dimensional Euler equations in singular domains. In Gérard-Varet and Lacave (Arch Ration Mech Anal 209(1):131-170, 2013), we have established the existence of weak solutions for a large class of bounded domains, with initial vorticity in L p (p>1). For unbounded domains, we have proved a similar result only when the initial vorticity is in $${L^{p}_{c}}$$ L c p (p>2) and when the domain is the exterior of a single obstacle. The goal here is to retrieve these two restrictions: we consider general initial vorticity in $${L^{1} {\cap} L^{p}}$$ L 1 ∩ L p (p>1), outside an arbitrary number of obstacles (not reduced to points). Springer-Verlag Berlin Heidelberg, 2015 Gérard-Varet David Univ Paris Diderot, Sorbonne Paris Cité, Institut de Mathématiques de Jussieu-Paris Rive Gauche, UMR 7586, CNRS, Sorbonne Universités, UPMC Univ Paris 06, 75013, Paris, France aut Lacave Christophe Univ Paris Diderot, Sorbonne Paris Cité, Institut de Mathématiques de Jussieu-Paris Rive Gauche, UMR 7586, CNRS, Sorbonne Universités, UPMC Univ Paris 06, 75013, Paris, France aut Archive for Rational Mechanics and Analysis Springer Berlin Heidelberg 218/3(2015-12-01), 1609-1631 0003-9527 218:3<1609 2015 218 205 https://doi.org/10.1007/s00205-015-0889-3 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00205-015-0889-3 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Gérard-Varet David Univ Paris Diderot, Sorbonne Paris Cité, Institut de Mathématiques de Jussieu-Paris Rive Gauche, UMR 7586, CNRS, Sorbonne Universités, UPMC Univ Paris 06, 75013, Paris, France aut NATIONALLICENCE 700 1- Lacave Christophe Univ Paris Diderot, Sorbonne Paris Cité, Institut de Mathématiques de Jussieu-Paris Rive Gauche, UMR 7586, CNRS, Sorbonne Universités, UPMC Univ Paris 06, 75013, Paris, France aut NATIONALLICENCE 773 0- Archive for Rational Mechanics and Analysis Springer Berlin Heidelberg 218/3(2015-12-01), 1609-1631 0003-9527 218:3<1609 2015 218 205 SWISSBIB 510008194