Existence and regularity of steady-state solutions of the Navier-Stokes equations arising from irregular data

2022/09/27 by Gael Yomgne Diebou, Diebou, Gael Y.
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.2209.13719

openalex publication_date 2022/09/27 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

We analyze the forced incompressible stationary Navier-Stokes flow in ℝⁿ₊, n>2. Existence of a unique solution satisfying a global integrabilty property measured in a scale of tent spaces is established for small data in homogenous Sobolev space with s=-(1)/(2) degree of smoothness. Moreover, the velocity field is shown to be locally Hölder continuous while the pressure belongs to L^p_loc for any p∈ (1,∞). Our approach is based on the analysis of the inhomogeneous Stokes system for which we derive a new solvability result involving Dirichlet data in Triebel-Lizorkin classes with negative amount of smoothness and is of independent interest.

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