On time analyticity of the Navier-Stokes equations in a rotating frame with spatially almost periodic data

Yoshikazu Giga; Hideaki Jo; Alex Mahalov; Tsuyoshi Yoneda

doi:10.1016/j.physd.2008.03.007

On time analyticity of the Navier-Stokes equations in a rotating frame with spatially almost periodic data

Yoshikazu Giga, Hideaki Jo, Alex Mahalov, Tsuyoshi Yoneda

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

13 Scopus citations

Abstract

We consider the Navier-Stokes equations with the Coriolis force when initial data may not decrease at spatial infinity so that almost periodic data is allowed. We prove that the local-in-time solution is analytic in time when initial data are in F M₀, the Fourier preimage of the space of all finite Radon measures with no point mass at the origin. When the initial data are almost periodic, this implies that the complex amplitude is analytic in time. In particular, a new mode cannot be created at any positive time.

Original language	English (US)
Pages (from-to)	1422-1428
Number of pages	7
Journal	Physica D: Nonlinear Phenomena
Volume	237
Issue number	10-12
DOIs	https://doi.org/10.1016/j.physd.2008.03.007
State	Published - Jul 15 2008

Keywords

Analyticity
Coriolis force
Frequency set
Navier-Stokes equations

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics
Condensed Matter Physics
Applied Mathematics

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10.1016/j.physd.2008.03.007

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title = "On time analyticity of the Navier-Stokes equations in a rotating frame with spatially almost periodic data",

abstract = "We consider the Navier-Stokes equations with the Coriolis force when initial data may not decrease at spatial infinity so that almost periodic data is allowed. We prove that the local-in-time solution is analytic in time when initial data are in F M0, the Fourier preimage of the space of all finite Radon measures with no point mass at the origin. When the initial data are almost periodic, this implies that the complex amplitude is analytic in time. In particular, a new mode cannot be created at any positive time.",

keywords = "Analyticity, Coriolis force, Frequency set, Navier-Stokes equations",

author = "Yoshikazu Giga and Hideaki Jo and Alex Mahalov and Tsuyoshi Yoneda",

note = "Funding Information: The work of the first author was partly supported by the Grant-in-Aid for Scientific Research, No. 18204011, No. 17654037, the Japan Society of the Promotion of Science (JSPS). He was also partly supported by the Grant-in-Aid for formation of COE {\textquoteright}Mathematics of Nonlinear Structures via Singularities{\textquoteright} (Hokkaido University) sponsored by JSPS. The work of the third author was partly supported by AFOSR contract FA9550-05-1-0047. The work of the fourth author was partly supported by the Grant-in-Aid for JSPS Fellows. ",

year = "2008",

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doi = "10.1016/j.physd.2008.03.007",

language = "English (US)",

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T1 - On time analyticity of the Navier-Stokes equations in a rotating frame with spatially almost periodic data

AU - Giga, Yoshikazu

AU - Jo, Hideaki

AU - Mahalov, Alex

AU - Yoneda, Tsuyoshi

N1 - Funding Information: The work of the first author was partly supported by the Grant-in-Aid for Scientific Research, No. 18204011, No. 17654037, the Japan Society of the Promotion of Science (JSPS). He was also partly supported by the Grant-in-Aid for formation of COE ’Mathematics of Nonlinear Structures via Singularities’ (Hokkaido University) sponsored by JSPS. The work of the third author was partly supported by AFOSR contract FA9550-05-1-0047. The work of the fourth author was partly supported by the Grant-in-Aid for JSPS Fellows.

PY - 2008/7/15

Y1 - 2008/7/15

N2 - We consider the Navier-Stokes equations with the Coriolis force when initial data may not decrease at spatial infinity so that almost periodic data is allowed. We prove that the local-in-time solution is analytic in time when initial data are in F M0, the Fourier preimage of the space of all finite Radon measures with no point mass at the origin. When the initial data are almost periodic, this implies that the complex amplitude is analytic in time. In particular, a new mode cannot be created at any positive time.

AB - We consider the Navier-Stokes equations with the Coriolis force when initial data may not decrease at spatial infinity so that almost periodic data is allowed. We prove that the local-in-time solution is analytic in time when initial data are in F M0, the Fourier preimage of the space of all finite Radon measures with no point mass at the origin. When the initial data are almost periodic, this implies that the complex amplitude is analytic in time. In particular, a new mode cannot be created at any positive time.

KW - Analyticity

KW - Coriolis force

KW - Frequency set

KW - Navier-Stokes equations

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SP - 1422

EP - 1428

JO - Physica D: Nonlinear Phenomena

JF - Physica D: Nonlinear Phenomena

IS - 10-12

ER -

On time analyticity of the Navier-Stokes equations in a rotating frame with spatially almost periodic data

Abstract

Keywords

ASJC Scopus subject areas

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