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

^*Corresponding author for this work

School of Fundamental Science and Engineering

Research output: Contribution to journal › Article › peer-review

7 Citations (Scopus)

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 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.

Original language	English
Article number	103339
Journal	Nonlinear Analysis: Real World Applications
Volume	61
DOIs	https://doi.org/10.1016/j.nonrwa.2021.103339
Publication status	Published - 2021 Oct

Keywords

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

ASJC Scopus subject areas

Analysis
Engineering(all)
Economics, Econometrics and Finance(all)
Computational Mathematics
Applied Mathematics

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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",

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

Abstract

Keywords

ASJC Scopus subject areas

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