The growth mechanism of boundary layers for the 2D Navier-Stokes equations

2022/03/06 by Fei Wang, Wang, Fei, Zhu Yichun +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2203.02996

openalex publication_date 2022/03/06 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28

Abstract

We give a detailed description of formation of the boundary layers in the inviscid limit problem. To be more specific, we prove that the magnitude of the vorticity near the boundary is growing to the size of 1/√ν and the width of the layer is spreading out to be proportional the √ν in a finite time period. In fact, the growth time scaling is almost ν

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