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arXiv · 2406.05329

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

Ning Liu·Yanlin Liu·Ping Zhang
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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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Ning Liu, Yanlin Liu, Ping Zhang. 2024-06-08. Global stability of large Fourier mode for 3-D anisotropic Navier-Stokes equations in cylindrical domain. https://arxiv.org/abs/2406.05329

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