On a 3D Stokes eigenvalue problem under Navier slip-with-friction boundary conditions and applications to Navier-Stokes equations

2024/07/10 by Luigi C. Berselli, Berselli, Luigi C., Alessio Falocchi +3
Chemical Engineering · Computer Science · Engineering · #Analysis of PDEs (math.AP) #Contact Mechanics and Variational Inequalities #Elasticity and Material Modeling #FOS: Mathematics #Primary 35Q30 #Rheology and Fluid Dynamics Studies #Secondary 47A75 #Spectral Theory (math.SP)

paper · pdf · doi:10.48550/arxiv.2407.07496

openalex publication_date 2024/07/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we consider, by means of a precise spectral analysis, the 3D Navier-Stokes equations endowed with Navier slip-with-friction boundary conditions. We study the problem in a very simple geometric situation as the region between two parallel planes, with periodicity along the two planes. This setting, which is often used in the theory of boundary layers, requires some special treatment for what concerns the functional setting and allows us to characterize in a rather explicit manner eigenvalues and eigenfunctions of the associated Stokes problem. These, will be then used in order to identify infinite dimensional classes of data leading to global strong solutions for the corresponding evolution Navier-Stokes equations.

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