A Liouville Theorem for the Planer Navier-Stokes Equations with the No-Slip Boundary Condition and Its Application to a Geometric Regularity Criterion

Yoshikazu Giga; Pen Yuan Hsu; Yasunori Maekawa

doi:10.1080/03605302.2014.912662

A Liouville Theorem for the Planer Navier-Stokes Equations with the No-Slip Boundary Condition and Its Application to a Geometric Regularity Criterion

Yoshikazu Giga, Pen Yuan Hsu, Yasunori Maekawa

SCI - Mathematics

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

16 Citations (Scopus)

Abstract

We establish a Liouville type result for a backward global solution to the Navier-Stokes equations in the half plane with the no-slip boundary condition. No assumptions on spatial decay for the vorticity nor the velocity field are imposed. We study the vorticity equations instead of the original Navier-Stokes equations. As an application, we extend the geometric regularity criterion for the Navier-Stokes equations in the three-dimensional half space under the no-slip boundary condition.

Original language	English
Pages (from-to)	1906-1935
Number of pages	30
Journal	Communications in Partial Differential Equations
Volume	39
Issue number	10
DOIs	https://doi.org/10.1080/03605302.2014.912662
Publication status	Published - 2014 Oct

Keywords

Boundary conditions
Geometric regularity criterion
Liouville theorem
Navier-Stokes equations
Vorticity
Vorticity equations

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1080/03605302.2014.912662

Cite this

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title = "A Liouville Theorem for the Planer Navier-Stokes Equations with the No-Slip Boundary Condition and Its Application to a Geometric Regularity Criterion",

abstract = "We establish a Liouville type result for a backward global solution to the Navier-Stokes equations in the half plane with the no-slip boundary condition. No assumptions on spatial decay for the vorticity nor the velocity field are imposed. We study the vorticity equations instead of the original Navier-Stokes equations. As an application, we extend the geometric regularity criterion for the Navier-Stokes equations in the three-dimensional half space under the no-slip boundary condition.",

keywords = "Boundary conditions, Geometric regularity criterion, Liouville theorem, Navier-Stokes equations, Vorticity, Vorticity equations",

author = "Yoshikazu Giga and Hsu, {Pen Yuan} and Yasunori Maekawa",

note = "Funding Information: The work of the first author is partly supported by the Japan Society of the Promotion of Science (JSPS) through grants Kiban (S) 21224001, Kiban (A) 23244015 and Houga 25610025. The work of the third author is partly supported by JSPS through Grant-in-Aid for Young Scientists (B) 25800079.",

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AU - Hsu, Pen Yuan

AU - Maekawa, Yasunori

N1 - Funding Information: The work of the first author is partly supported by the Japan Society of the Promotion of Science (JSPS) through grants Kiban (S) 21224001, Kiban (A) 23244015 and Houga 25610025. The work of the third author is partly supported by JSPS through Grant-in-Aid for Young Scientists (B) 25800079.

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N2 - We establish a Liouville type result for a backward global solution to the Navier-Stokes equations in the half plane with the no-slip boundary condition. No assumptions on spatial decay for the vorticity nor the velocity field are imposed. We study the vorticity equations instead of the original Navier-Stokes equations. As an application, we extend the geometric regularity criterion for the Navier-Stokes equations in the three-dimensional half space under the no-slip boundary condition.

AB - We establish a Liouville type result for a backward global solution to the Navier-Stokes equations in the half plane with the no-slip boundary condition. No assumptions on spatial decay for the vorticity nor the velocity field are imposed. We study the vorticity equations instead of the original Navier-Stokes equations. As an application, we extend the geometric regularity criterion for the Navier-Stokes equations in the three-dimensional half space under the no-slip boundary condition.

KW - Boundary conditions

KW - Geometric regularity criterion

KW - Liouville theorem

KW - Navier-Stokes equations

KW - Vorticity

KW - Vorticity equations

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JO - Communications in Partial Differential Equations

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A Liouville Theorem for the Planer Navier-Stokes Equations with the No-Slip Boundary Condition and Its Application to a Geometric Regularity Criterion

Abstract

Keywords

ASJC Scopus subject areas

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