Large time behavior for solutions to the anisotropic Navier-Stokes equations in a 3D half-space

2024/10/07 by Mikihiro Fujii, Yang Li, Fujii, Mikihiro +1
Engineering · Mathematics · #35B40 #35Q30 #35Q35 #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2410.04904

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

Abstract

We consider the large time behavior of the solution to the anisotropic Navier--Stokes equations in a 3D half-space. Investigating the precise anisotropic nature of linearized solutions, we obtain the optimal decay estimates for the nonlinear global solutions in anisotropic Lebesgue norms. In particular, we reveal the enhanced dissipation mechanism for the third component of velocity field. We notice that, in contrast to the whole space case, some difficulties arises on the L¹(ℝ³₊)-estimates of the solution due to the nonlocal operators appearing in the linear solution formula. To overcome this, we introduce suitable Besov type spaces and employ the Littlewood--Paley analysis on the tangential space.

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