Stability of singular solutions to the Navier-Stokes system

被引：5

作者：

Cannone, Marco ^{[1
]}

Karch, Grzegorz ^{[2
]}

Pilarczyk, Dominika ^{[3
]}

Wu, Gang ^{[4
]}

机构：

[1] Univ Gustave Eiffel, Lab Anal & Math Appl, 5 Blvd Descartes, F-77420 Champs Sur Marne, Marne, France

[2] Univ Wroclawski, Inst Matematyczny, Pl Grunwaldzki 2-4, PL-50384 Wroclaw, Poland

[3] Wydzial Matemat, Politech Wroclawska, Wybrzeze Wyspianskiego 37, Wroclaw, Poland

[4] Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2022年 / 314卷

基金：

中国国家自然科学基金;

关键词：

Navier-Stokes equation; Cauchy problem; Stationary solutions; Singular solutions; Asymptotic behavior of  solutions; STEADY-STATE SOLUTIONS; HOMOGENEOUS SOLUTIONS; EXTERNAL FORCES; ASYMPTOTIC-BEHAVIOR; FINITE-ENERGY; LP-SOLUTIONS; EQUATIONS; STATIONARY; EXISTENCE; SPACES;

D O I：

10.1016/j.jde.2022.01.010

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We develop mathematical methods which allow us to study asymptotic properties of solutions to the three dimensional Navier-Stokes system for incompressible fluid in the whole three dimensional space. We deal either with the Cauchy problem or with the stationary problem where solutions may be singular due to singular external forces which are either singular finite measures or more general tempered distributions with bounded Fourier transforms. We present results on asymptotic properties of such solutions either for large values of the space variables (so called the far-field asymptotics) or for large values of time. (c) 2022 Elsevier Inc. All rights reserved.

引用

页码：316 / 339

页数：24

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