Existence of strong solutions and decay of turbulent solutions of Navier–Stokes flow with nonzero Dirichlet boundary data

Reinhard Farwig; Hideo Kozono; David Wegmann

doi:10.1016/j.jmaa.2017.03.086

Existence of strong solutions and decay of turbulent solutions of Navier–Stokes flow with nonzero Dirichlet boundary data

Reinhard Farwig, Hideo Kozono, David Wegmann^*

^*Corresponding author for this work

School of Fundamental Science and Engineering

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

1 Citation (Scopus)

Abstract

Recently, Leray's problem of the L²-decay of a special weak solution to the Navier–Stokes equations with nonhomogeneous boundary values was studied by the authors, exploiting properties of the approximate solutions converging to this solution. In this paper this result is generalized to the case of an arbitrary weak solution satisfying the strong energy inequality.

Original language	English
Pages (from-to)	271-286
Number of pages	16
Journal	Journal of Mathematical Analysis and Applications
Volume	453
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2017.03.086
Publication status	Published - 2017 Sep 1

Keywords

Asymptotic behavior
Exterior domain
Instationary Navier–Stokes equations
Nonzero boundary values
Time-dependent data
Weak solutions

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.jmaa.2017.03.086

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title = "Existence of strong solutions and decay of turbulent solutions of Navier–Stokes flow with nonzero Dirichlet boundary data",

abstract = "Recently, Leray's problem of the L2-decay of a special weak solution to the Navier–Stokes equations with nonhomogeneous boundary values was studied by the authors, exploiting properties of the approximate solutions converging to this solution. In this paper this result is generalized to the case of an arbitrary weak solution satisfying the strong energy inequality.",

keywords = "Asymptotic behavior, 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: The second author H. K. was supported by the Japanese?German Graduate Externship on Mathematical Fluid Dynamics funded by JSPS. Publisher Copyright: {\textcopyright} 2017 Elsevier Inc.",

year = "2017",

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doi = "10.1016/j.jmaa.2017.03.086",

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journal = "Journal of Mathematical Analysis and Applications",

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T1 - Existence of strong solutions and decay of turbulent solutions of Navier–Stokes flow with nonzero Dirichlet boundary data

AU - Farwig, Reinhard

AU - Kozono, Hideo

AU - Wegmann, David

PY - 2017/9/1

Y1 - 2017/9/1

N2 - Recently, Leray's problem of the L2-decay of a special weak solution to the Navier–Stokes equations with nonhomogeneous boundary values was studied by the authors, exploiting properties of the approximate solutions converging to this solution. In this paper this result is generalized to the case of an arbitrary weak solution satisfying the strong energy inequality.

AB - Recently, Leray's problem of the L2-decay of a special weak solution to the Navier–Stokes equations with nonhomogeneous boundary values was studied by the authors, exploiting properties of the approximate solutions converging to this solution. In this paper this result is generalized to the case of an arbitrary weak solution satisfying the strong energy inequality.

KW - Asymptotic behavior

KW - Exterior domain

KW - Instationary Navier–Stokes equations

KW - Nonzero boundary values

KW - Time-dependent data

KW - Weak solutions

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VL - 453

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EP - 286

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

IS - 1

ER -

Existence of strong solutions and decay of turbulent solutions of Navier–Stokes flow with nonzero Dirichlet boundary data

Abstract

Keywords

ASJC Scopus subject areas

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