Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

HOME ALL ARTICLES View

Bull. Korean Math. Soc. 2024; 61(3): 637-669

Online first article April 19, 2024      Printed May 31, 2024

https://doi.org/10.4134/BKMS.b230297

Copyright © The Korean Mathematical Society.

Decay results of weak solutions to the non-stationary fractional Navier-Stokes equations

Zhaoxia Liu

Minzu University of China

Abstract

The goal of this paper is to study decay properties of weak solutions to Cauchy problem of the non-stationary fractional Navier-Stokes equations. By using the Fourier splitting method, we give the time $L^2$-decay rate of weak solutions, which reveals that $L^2$-decay is generally determined by its linear generalized Stokes flow. In second part, we establish various decay results and the uniqueness of the two dimensional fractional Navier-Stokes flows. In the end of this article, as an appendix, the existence of global weak solutions is given by making use of Galerkin' method, weak and strong compact convergence theorems.

Keywords: Fractional Navier-Stokes equations, Fourier splitting method, weak solution

MSC numbers: 35Q30, 76D03, 76D05

Supported by: This work is supported by NSF of China under Grant No. 12371123.