2018年2月
Navier-Stokes equations with external forces in Lorentz spaces and its application to the self-similar solutions
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
- ,
- 巻
- 458
- 号
- 2
- 開始ページ
- 1693
- 終了ページ
- 1708
- 記述言語
- 英語
- 掲載種別
- 研究論文(学術雑誌)
- DOI
- 10.1016/j.jmaa.2017.10.048
- 出版者・発行元
- ACADEMIC PRESS INC ELSEVIER SCIENCE
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.
- リンク情報
- ID情報
-
- DOI : 10.1016/j.jmaa.2017.10.048
- ISSN : 0022-247X
- eISSN : 1096-0813
- Web of Science ID : WOS:000417771900045