Global stability of large Fourier mode for 3-D anisotropic Navier-Stokes equations in cylindrical domain

2024/06/08 by Ning Liu, Y. Liu, Liu, Ning +3
Engineering · Mathematics · #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.2406.05329

openalex publication_date 2024/06/08 · openalex created_date 2024/06/12 · openalex updated_date 2026/07/28

Abstract

In this paper, we first establish the global existence and stability of solutions to 3-D classical Navier-Stokes equations (NS) in an infinite cylindrical domain with large Fourier mode initial data. Then we extend similar result for 3-D anisotropic Navier-Stokes equations (ANS). We remark that due to the loss of vertical viscosity in (ANS), the construction of the energy functionals for (ANS) is much more subtle than that of (NS). Compared with our previous paper for (NS), we improve the polynomial decay in k for the Fourier coefficients of the solution to be exponential decay in k here.

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