Stationary solution to the Navier-Stokes equations in the scaling invariant Besov space and its regularity

Kenta Kaneko, Hideo Kozono, Senjo Shimizu

研究成果: Article査読

3 被引用数 (Scopus)

抄録

We consider the stationary problem of the Navier-Stokes equations in ℝn for n ≥ 3. We show existence, uniqueness, and regularity of solutions in the homogeneous Besov space Ḃp,q−1+n/p, which is the scaling invariant one. As a corollary of our results, a self-similar solution is obtained. For the proof, several bilinear estimates are established. The essential tool is based on the paraproduct formula and the imbedding theorem in homogeneous Besov spaces.

本文言語English
ページ(範囲)857-880
ページ数24
ジャーナルIndiana University Mathematics Journal
68
3
DOI
出版ステータスPublished - 2019

ASJC Scopus subject areas

  • 数学 (全般)

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