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

Hideo Kozono*, Senjo Shimizu

*この研究の対応する著者

研究成果: Article査読

5 被引用数 (Scopus)

抄録

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.

本文言語English
ページ(範囲)1693-1708
ページ数16
ジャーナルJournal of Mathematical Analysis and Applications
458
2
DOI
出版ステータスPublished - 2018 2 15

ASJC Scopus subject areas

  • 分析
  • 応用数学

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