The Two-Dimensional Euler Equations on Singular Domains
Identifieur interne : 000011 ( France/Analysis ); précédent : 000010; suivant : 000012The Two-Dimensional Euler Equations on Singular Domains
Auteurs : David Gérard-Varet [France] ; Christophe Lacave [France]Source :
- Archive for Rational Mechanics and Analysis [ 0003-9527 ] ; 2013-07-01.
Abstract
Abstract: We establish the existence of global weak solutions of the two-dimensional incompressible Euler equations for a large class of non-smooth open sets. Loosely, these open sets are the complements (in a simply connected domain) of a finite number of obstacles with positive Sobolev capacity. Existence of weak solutions with L p vorticity is deduced from a property of domain continuity for the Euler equations that relates to the so-called γ-convergence of open sets. Our results complete those obtained for convex domains in Taylor (Progress in Nonlinear Differential Equations and their Applications, Vol. 42, 2000), or for domains with asymptotically small holes (Iftimie et al. in Commun Partial Differ Equ 28(1–2), 349–379, 2003; Lopes Filho in SIAM J Math Anal 39(2), 422–436, 2007).
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DOI: 10.1007/s00205-013-0617-9
Affiliations:
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Loosely, these open sets are the complements (in a simply connected domain) of a finite number of obstacles with positive Sobolev capacity. Existence of weak solutions with L p vorticity is deduced from a property of domain continuity for the Euler equations that relates to the so-called γ-convergence of open sets. Our results complete those obtained for convex domains in Taylor (Progress in Nonlinear Differential Equations and their Applications, Vol. 42, 2000), or for domains with asymptotically small holes (Iftimie et al. in Commun Partial Differ Equ 28(1–2), 349–379, 2003; Lopes Filho in SIAM J Math Anal 39(2), 422–436, 2007).</div></front></TEI><affiliations><list><country><li>France</li></country><region><li>Île-de-France</li></region><settlement><li>Paris</li></settlement></list><tree><country name="France"><region name="Île-de-France"><name sortKey="Gerard Varet, David" sort="Gerard Varet, David" uniqKey="Gerard Varet D" first="David" last="Gérard-Varet">David Gérard-Varet</name></region><name sortKey="Gerard Varet, David" sort="Gerard Varet, David" uniqKey="Gerard Varet D" first="David" last="Gérard-Varet">David Gérard-Varet</name><name sortKey="Lacave, Christophe" sort="Lacave, Christophe" uniqKey="Lacave C" first="Christophe" last="Lacave">Christophe Lacave</name><name sortKey="Lacave, Christophe" sort="Lacave, Christophe" uniqKey="Lacave C" first="Christophe" last="Lacave">Christophe Lacave</name></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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