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arXiv · 2303.05236

Layer separation of the 3D incompressible Navier-Stokes equation in a bounded domain

Alexis F. Vasseur·Jincheng Yang
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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.

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Alexis F. Vasseur, Jincheng Yang. 2023-03-09. Layer separation of the 3D incompressible Navier-Stokes equation in a bounded domain. https://doi.org/10.1080/03605302.2024.2346146

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