On a Stationary Problem of the Stokes Equation in an Infinite Layer in Sobolev and Besov Spaces

Takayuki Abe; Masao Yamazaki

doi:10.1007/s00021-008-0276-z

On a Stationary Problem of the Stokes Equation in an Infinite Layer in Sobolev and Besov Spaces

Takayuki Abe^*, Masao Yamazaki

^*Corresponding author for this work

School of Fundamental Science and Engineering

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

3 Citations (Scopus)

Abstract

This paper is concerned with the stationary problem of the Stokes equation in an infinite layer and provides a condition on the external force sufficient for the existence of the solution. Since the Poiseuille flow is a solution to the homogeneous equation, the solution is not unique when p = ∞. It is also proved that, under some suitable conditions, solutions to the homogeneous equation are limited only to the Poiseuille flow.

Original language	English
Pages (from-to)	61-100
Number of pages	40
Journal	Journal of Mathematical Fluid Mechanics
Volume	12
Issue number	1
DOIs	https://doi.org/10.1007/s00021-008-0276-z
Publication status	Published - 2010 Mar

Keywords

Besov space
Homogeneous Besov space
Infinite layer
Poiseuille flow
Sobolev space
Stationary problem
Stokes equation

ASJC Scopus subject areas

Mathematical Physics
Condensed Matter Physics
Computational Mathematics
Applied Mathematics

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10.1007/s00021-008-0276-z

Cite this

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abstract = "This paper is concerned with the stationary problem of the Stokes equation in an infinite layer and provides a condition on the external force sufficient for the existence of the solution. Since the Poiseuille flow is a solution to the homogeneous equation, the solution is not unique when p = ∞. It is also proved that, under some suitable conditions, solutions to the homogeneous equation are limited only to the Poiseuille flow.",

keywords = "Besov space, Homogeneous Besov space, Infinite layer, Poiseuille flow, Sobolev space, Stationary problem, Stokes equation",

author = "Takayuki Abe and Masao Yamazaki",

note = "Funding Information: ∗Partly supported by the Grant-in-Aid for Young Scientists (B) 17740072, The Ministry of Education, Culture, Sports, Science and Technology, Japan. †Partly supported by the Grant-in-Aid for Scientific Research (C) 17540174, Japan Society for the Promotion of Science.",

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doi = "10.1007/s00021-008-0276-z",

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AU - Abe, Takayuki

AU - Yamazaki, Masao

N1 - Funding Information: ∗Partly supported by the Grant-in-Aid for Young Scientists (B) 17740072, The Ministry of Education, Culture, Sports, Science and Technology, Japan. †Partly supported by the Grant-in-Aid for Scientific Research (C) 17540174, Japan Society for the Promotion of Science.

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N2 - This paper is concerned with the stationary problem of the Stokes equation in an infinite layer and provides a condition on the external force sufficient for the existence of the solution. Since the Poiseuille flow is a solution to the homogeneous equation, the solution is not unique when p = ∞. It is also proved that, under some suitable conditions, solutions to the homogeneous equation are limited only to the Poiseuille flow.

AB - This paper is concerned with the stationary problem of the Stokes equation in an infinite layer and provides a condition on the external force sufficient for the existence of the solution. Since the Poiseuille flow is a solution to the homogeneous equation, the solution is not unique when p = ∞. It is also proved that, under some suitable conditions, solutions to the homogeneous equation are limited only to the Poiseuille flow.

KW - Besov space

KW - Homogeneous Besov space

KW - Infinite layer

KW - Poiseuille flow

KW - Sobolev space

KW - Stationary problem

KW - Stokes equation

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On a Stationary Problem of the Stokes Equation in an Infinite Layer in Sobolev and Besov Spaces

Abstract

Keywords

ASJC Scopus subject areas

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