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

Kenta Kaneko, Hideo Kozono, Senjo Shimizu

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)857-880
Number of pages24
JournalIndiana University Mathematics Journal
Volume68
Issue number3
DOIs
Publication statusPublished - 2019

ASJC Scopus subject areas

  • Mathematics(all)

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