Decay of non-stationary navier-stokes flow with nonzero dirichlet boundary data

Reinhard Farwig; Hideo Kozono; David Wegmann

doi:10.1512/iumj.2017.66.6163

Decay of non-stationary navier-stokes flow with nonzero dirichlet boundary data

Reinhard Farwig, Hideo Kozono, David Wegmann

Mathematical Science Center for Co-creative Society (MathCCS)

Technische Universität Darmstadt

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

Abstract

Consider the Navier-Stokes equations in a domain with compact boundary and nonzero Dirichlet boundary data. Recently, the first two authors of this article and F. Riechwald showed for an exterior domain the existence of weak solutions of Leray-Hopf type. Starting from the proof of existence, we will get a weak solution satisfying kv(t)k2 → 0 as t → ∞, and determine an upper bound for the decay rate.

Original language	English
Pages (from-to)	2169-2185
Number of pages	17
Journal	Indiana University Mathematics Journal
Volume	66
Issue number	6
DOIs	https://doi.org/10.1512/iumj.2017.66.6163
Publication status	Published - 2017

Keywords

Asymptotic behaviour
Bounded domain
Exterior domain
Instationary navier-stokes equations
Nonzero boundary values
Time-dependent data
Weak solutions

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10.1512/iumj.2017.66.6163

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title = "Decay of non-stationary navier-stokes flow with nonzero dirichlet boundary data",

abstract = "Consider the Navier-Stokes equations in a domain with compact boundary and nonzero Dirichlet boundary data. Recently, the first two authors of this article and F. Riechwald showed for an exterior domain the existence of weak solutions of Leray-Hopf type. Starting from the proof of existence, we will get a weak solution satisfying kv(t)k2 → 0 as t → ∞, and determine an upper bound for the decay rate.",

keywords = "Asymptotic behaviour, Bounded domain, Exterior domain, Instationary navier-stokes equations, Nonzero boundary values, Time-dependent data, Weak solutions",

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

note = "Funding Information: Acknowledgements. The first and third authors greatly acknowledge the support of the EU Project FLUX, International Research Staff Exchange Scheme, FP7-PEOPLE-2011-IRSES. The second author was supported by the International Research Training Group (IRTG 1529) on Mathematical Fluid Dynamics, funded by Deutsche Forschungsgemeinschaft and the Japan Society for Promotion of Science.",

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language = "English",

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AU - Farwig, Reinhard

AU - Kozono, Hideo

AU - Wegmann, David

N1 - Funding Information: Acknowledgements. The first and third authors greatly acknowledge the support of the EU Project FLUX, International Research Staff Exchange Scheme, FP7-PEOPLE-2011-IRSES. The second author was supported by the International Research Training Group (IRTG 1529) on Mathematical Fluid Dynamics, funded by Deutsche Forschungsgemeinschaft and the Japan Society for Promotion of Science.

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N2 - Consider the Navier-Stokes equations in a domain with compact boundary and nonzero Dirichlet boundary data. Recently, the first two authors of this article and F. Riechwald showed for an exterior domain the existence of weak solutions of Leray-Hopf type. Starting from the proof of existence, we will get a weak solution satisfying kv(t)k2 → 0 as t → ∞, and determine an upper bound for the decay rate.

AB - Consider the Navier-Stokes equations in a domain with compact boundary and nonzero Dirichlet boundary data. Recently, the first two authors of this article and F. Riechwald showed for an exterior domain the existence of weak solutions of Leray-Hopf type. Starting from the proof of existence, we will get a weak solution satisfying kv(t)k2 → 0 as t → ∞, and determine an upper bound for the decay rate.

KW - Asymptotic behaviour

KW - Bounded domain

KW - Exterior domain

KW - Instationary navier-stokes equations

KW - Nonzero boundary values

KW - Time-dependent data

KW - Weak solutions

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JO - Indiana University Mathematics Journal

JF - Indiana University Mathematics Journal

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Decay of non-stationary navier-stokes flow with nonzero dirichlet boundary data

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