Communications in Mathematical Sciences

Volume 22 (2024)

Number 2

Global existence of perturbed Navier–Stokes system around Landau solutions with slowly decaying oscillation

Pages: 533 – 561

DOI: https://dx.doi.org/10.4310/CMS.2024.v22.n2.a10

Authors

Jiayan Wu (School of Mathematical Sciences, Zhejiang University, Hangzhou, China)

Cuili Zhai (School of Mathematics and Physics, University of Science and Technology, Beijing, China)

Jingjing Zhang (School of Mathematical Sciences, Zhejiang University, Hangzhou, China)

Ting Zhang (School of Mathematical Sciences, Zhejiang University, Hangzhou, China)

Abstract

In this paper, we consider the perturbed Navier–Stokes system around the Landau solutions. Using the energy method and the continuation method, we show the global existence of the $L^2$ local energy solution for the perturbed Navier–Stokes system with the oscillation decay initial data $v_0 \in E^2_{\sigma} + L^3_{\operatorname{uloc}} \,$.

Keywords

global existence, Navier–Stokes system, Landau solutions

2010 Mathematics Subject Classification

35A01, 35Q30, 49K40

Full Text (PDF format)

The work of Ting Zhang is partially supported by the National Natural Science Foundation of China 11931010, and Zhejiang Provincial Natural Science Foundation of China LDQ23A010001. Cuili Zhai is partially supported by the NSF of China under Grant 12201035.

Received 28 January 2022

Received revised 16 July 2023

Accepted 18 July 2023

Published 1 February 2024