Work

Large Time Behavior for Solutions to the Anisotropic Navier–Stokes Equations in a 3D Half-space

Year: 2024

Type: article

Abstract: We consider the large time behavior of the solution to the anisotropic Navier–Stokes equations in a $3$D 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 $L^{1}(\mathbb{R}^{3}_{+})$-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.

Source: International Mathematics Research Notices

DOI: 10.1093/imrn/rnae265

Authors: Mikihiro Fujii, Yang Li

Institutions: Nagoya City University, Anhui University

Language: English

Topic: Navier-Stokes equation solutions

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Japan Society for the Promotion of Science, Natural Science Foundation of Anhui Province

Awards: Mathematical analysis for the compressible viscous rotating flow, G3402004506