Current browse context:
math.AP
Change to browse by:
References & Citations
Mathematics > Analysis of PDEs
Title: Layer separation of the 3D incompressible Navier-Stokes equation in a bounded domain
(Submitted on 9 Mar 2023 (v1), last revised 26 Apr 2024 (this version, v2))
Abstract: We provide an unconditional $L^2$ upper bound for the boundary layer separation of Leray-Hopf solutions in a smooth bounded domain. By layer separation, we mean the discrepancy between a (turbulent) low-viscosity Leray-Hopf solution $u^\nu$ and a fixed (laminar) regular Euler solution $\bar u$ with similar initial conditions and body force. We show an asymptotic upper bound $C \|\bar u\|_{L^\infty}^3 T$ on the layer separation, anomalous dissipation, and the work done by friction. This extends the previous result when the Euler solution is a regular shear in a finite channel. The key estimate is to control the boundary vorticity in a way that does not degenerate in the vanishing viscosity limit.
Submission history
From: Jincheng Yang [view email][v1] Thu, 9 Mar 2023 13:19:14 GMT (160kb)
[v2] Fri, 26 Apr 2024 16:22:58 GMT (163kb,D)
Link back to: arXiv, form interface, contact.