The time periodic problem of the Navier–Stokes equations in a bounded domain with moving boundary

Reinhard Farwig; Hideo Kozono; Kazuyuki Tsuda; David Wegmann

doi:10.1016/j.nonrwa.2021.103339

The time periodic problem of the Navier–Stokes equations in a bounded domain with moving boundary

Reinhard Farwig^*, Hideo Kozono, Kazuyuki Tsuda, David Wegmann

^*この研究の対応する著者

基幹理工学部

研究成果: Article › 査読

抄録

The time periodic problem of the Navier–Stokes equations on a non-cylindrical space–time domain is studied. Motivated by a recent result by Saal (2006) on maximal regularity for this kind of system we construct time periodic solutions in L^q-spaces provided the bounded domain moves periodically with small amplitude and the given periodic external force is small. The proof is based on new decay estimates for the solution operator of parabolic evolution equations corresponding to the non-cylindrical space–time domain problem.

本文言語	English
論文番号	103339
ジャーナル	Nonlinear Analysis: Real World Applications
巻	61
DOI	https://doi.org/10.1016/j.nonrwa.2021.103339
出版ステータス	Published - 2021 10

ASJC Scopus subject areas

分析
工学（全般）
経済学、計量経済学および金融学（全般）
計算数学
応用数学

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10.1016/j.nonrwa.2021.103339

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title = "The time periodic problem of the Navier–Stokes equations in a bounded domain with moving boundary",

abstract = "The time periodic problem of the Navier–Stokes equations on a non-cylindrical space–time domain is studied. Motivated by a recent result by Saal (2006) on maximal regularity for this kind of system we construct time periodic solutions in Lq-spaces provided the bounded domain moves periodically with small amplitude and the given periodic external force is small. The proof is based on new decay estimates for the solution operator of parabolic evolution equations corresponding to the non-cylindrical space–time domain problem.",

keywords = "Moving boundary, Navier–Stokes equations, Non-cylindrical space–time domain, Time periodic problem, Uniform H-calculus",

author = "Reinhard Farwig and Hideo Kozono and Kazuyuki Tsuda and David Wegmann",

note = "Funding Information: The third author is partly supported by Grant-in-Aid for JSPS, Japan Fellows with Grant number A17J047780 . Publisher Copyright: {\textcopyright} 2021 Elsevier Ltd",

year = "2021",

month = oct,

doi = "10.1016/j.nonrwa.2021.103339",

language = "English",

volume = "61",

journal = "Nonlinear Analysis: Real World Applications",

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T1 - The time periodic problem of the Navier–Stokes equations in a bounded domain with moving boundary

AU - Farwig, Reinhard

AU - Kozono, Hideo

AU - Tsuda, Kazuyuki

AU - Wegmann, David

PY - 2021/10

Y1 - 2021/10

N2 - The time periodic problem of the Navier–Stokes equations on a non-cylindrical space–time domain is studied. Motivated by a recent result by Saal (2006) on maximal regularity for this kind of system we construct time periodic solutions in Lq-spaces provided the bounded domain moves periodically with small amplitude and the given periodic external force is small. The proof is based on new decay estimates for the solution operator of parabolic evolution equations corresponding to the non-cylindrical space–time domain problem.

AB - The time periodic problem of the Navier–Stokes equations on a non-cylindrical space–time domain is studied. Motivated by a recent result by Saal (2006) on maximal regularity for this kind of system we construct time periodic solutions in Lq-spaces provided the bounded domain moves periodically with small amplitude and the given periodic external force is small. The proof is based on new decay estimates for the solution operator of parabolic evolution equations corresponding to the non-cylindrical space–time domain problem.

KW - Moving boundary

KW - Navier–Stokes equations

KW - Non-cylindrical space–time domain

KW - Time periodic problem

KW - Uniform H-calculus

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DO - 10.1016/j.nonrwa.2021.103339

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VL - 61

JO - Nonlinear Analysis: Real World Applications

JF - Nonlinear Analysis: Real World Applications

SN - 1468-1218

M1 - 103339

ER -

The time periodic problem of the Navier–Stokes equations in a bounded domain with moving boundary

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