STRONG TIME-PERIODIC SOLUTIONS TO CHEMOTAXIS-NAVIER-STOKES EQUATIONS ON BOUNDED DOMAINS

Keiichi Watanabe*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

Consider the chemotaxis-Navier-Stokes equations on a bounded convex domain Ω ⊂ ℝ3, where the boundary ∂Ω of Ω is not necessarily smooth. It is shown that this system admits a unique strong 2π-periodic solution provided that given 2π-periodic forcing functions are sufficiently small in their natural norm. The result may extend to general cases ⊂ ℝd, d ≥ 2, if one additionally assumes that ∂Ω is of class C3. The nonnegativity of solutions is also discussed.

Original languageEnglish
Pages (from-to)5577-5590
Number of pages14
JournalDiscrete and Continuous Dynamical Systems- Series A
Volume42
Issue number11
DOIs
Publication statusPublished - 2022 Nov

Keywords

  • Arendt-Bu theorem
  • Chemotaxis{Navier{Stokes equations
  • convex domains
  • maximal regularity
  • strong periodic solution

ASJC Scopus subject areas

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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