Navier-Stokes equations with external forces in Lorentz spaces and its application to the self-similar solutions

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:458

Article

Kozono, Hideo¹  Shimizu, Senjo² 

[1] Waseda Univ, Dept Math, Tokyo 1698555, Japan

[2] Kyoto Univ, Grad Sch Human & Environm Studies, Kyoto 6068501, Japan

关键词: Navier-Stokes equations;    Self-similar solutions;    Lorentz space;    Maximal regularity theorem;    Global solutions;    Implicit function theorem;   

DOI  :  10.1016/j.jmaa.2017.10.048

来源: Elsevier

【 摘 要 】

We show existence theorem of global mild solutions with small initial data and external forces in Lorentz spaces with scaling invariant norms. If the initial data have more regularity in another scaling invariant class, then our mild solution is actually the strong solution. The result on local existence of solutions for large data is also discussed. Our method is based on the maximal regularity theorem on the Stokes equations in Lorentz spaces. Then we apply our theorem to prove existence of self-similar solutions provided both initial data and external forces are homogeneous functions. Since we construct the global solution by means of the implicit function theorem, as a byproduct, its stability with respect to the given data is necessarily obtained. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free