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

Keiichi Watanabe

doi:10.3934/dcds.2022114

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

Keiichi Watanabe^*

^*Corresponding author for this work

Global Center for Science and Engineering

Research output: Contribution to journal › Article › peer-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 ⊂ ℝ^d, d ≥ 2, if one additionally assumes that ∂Ω is of class C³. The nonnegativity of solutions is also discussed.

Original language	English
Pages (from-to)	5577-5590
Number of pages	14
Journal	Discrete and Continuous Dynamical Systems- Series A
Volume	42
Issue number	11
DOIs	https://doi.org/10.3934/dcds.2022114
Publication status	Published - 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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10.3934/dcds.2022114

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title = "STRONG TIME-PERIODIC SOLUTIONS TO CHEMOTAXIS-NAVIER-STOKES EQUATIONS ON BOUNDED DOMAINS",

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.",

keywords = "Arendt-Bu theorem, Chemotaxis{Navier{Stokes equations, convex domains, maximal regularity, strong periodic solution",

author = "Keiichi Watanabe",

note = "Funding Information: 2020 Mathematics Subject Classification. Primary: 92C17; Secondary: 35Q92. Key words and phrases. Chemotaxis–Navier–Stokes equations, convex domains, strong periodic solution, maximal regularity, Arendt-Bu theorem. The first author is supported by JSPS KAKENHI Grant Number 20K22311 and 21K13826 and Waseda University Grant for Special Research Projects (Project number; 2021C-583). ∗Corresponding author: Keiichi Watanabe. Publisher Copyright: {\textcopyright} 2022 American Institute of Mathematical Sciences. All rights reserved.",

year = "2022",

month = nov,

doi = "10.3934/dcds.2022114",

language = "English",

volume = "42",

pages = "5577--5590",

journal = "Discrete and Continuous Dynamical Systems- Series A",

issn = "1078-0947",

publisher = "Southwest Missouri State University",

number = "11",

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T1 - STRONG TIME-PERIODIC SOLUTIONS TO CHEMOTAXIS-NAVIER-STOKES EQUATIONS ON BOUNDED DOMAINS

AU - Watanabe, Keiichi

N1 - Funding Information: 2020 Mathematics Subject Classification. Primary: 92C17; Secondary: 35Q92. Key words and phrases. Chemotaxis–Navier–Stokes equations, convex domains, strong periodic solution, maximal regularity, Arendt-Bu theorem. The first author is supported by JSPS KAKENHI Grant Number 20K22311 and 21K13826 and Waseda University Grant for Special Research Projects (Project number; 2021C-583). ∗Corresponding author: Keiichi Watanabe. Publisher Copyright: © 2022 American Institute of Mathematical Sciences. All rights reserved.

PY - 2022/11

Y1 - 2022/11

N2 - 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.

AB - 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.

KW - Arendt-Bu theorem

KW - Chemotaxis{Navier{Stokes equations

KW - convex domains

KW - maximal regularity

KW - strong periodic solution

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EP - 5590

JO - Discrete and Continuous Dynamical Systems- Series A

JF - Discrete and Continuous Dynamical Systems- Series A

SN - 1078-0947

IS - 11

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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