Mathematics > Analysis of PDEs
[Submitted on 2 Aug 2018 (v1), last revised 12 Oct 2018 (this version, v2)]
Title:Remarks on the emergence of weak Euler solutions in the vanishing viscosity limit
View PDFAbstract:We prove that if the local second-order structure function exponents in the inertial range remain positive uniformly in viscosity, then any spacetime $L^2$ weak limit of Leray--Hopf weak solutions of the Navier-Stokes equations on any bounded domain $\Omega\subset \mathbb{R}^d$, $d= 2,3$ is a weak solution of the Euler equations. This holds for both no-slip and Navier-friction conditions with viscosity-dependent slip length. The result allows for the emergence of non-unique, possibly dissipative, limiting weak solutions of the Euler equations.
Submission history
From: Theodore Drivas D [view email][v1] Thu, 2 Aug 2018 20:39:17 UTC (13 KB)
[v2] Fri, 12 Oct 2018 17:54:28 UTC (15 KB)
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