The Two-Dimensional Euler Equations on Singular Domains
The Two-Dimensional Euler Equations on Singular Domains
复制标题
奇异域上的二维欧拉方程
DOI：
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发表时间：
2013
影响因子：
2.5
通讯作者：
C. Lacave
中科院分区：
文献类型：
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作者：
D. Gérard;C. Lacave
我们建立了一大类非光滑开集的二维不可压缩欧拉方程的全局弱解的存在性。松散地说，这些开集是有限数量具有正 Sobolev 容量的障碍物的补集（在单连通域中）。具有 Lp 涡度的弱解的存在性是从与所谓的开集 γ 收敛相关的欧拉方程的域连续性性质推导出来的。我们的结果完成了泰勒凸域（非线性微分方程及其应用的进展，第 42 卷，2000 年）或渐近小孔域（Iftimie 等人在 Commun Partial Differ Equ 28(1–2), 349–379, 2003；Lopes Filho 在 SIAM J Math Anal 39(2) 中获得的结果， 422-436，2007）。
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 Lp 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).