Strichartz estimates for the Euler equations in the rotational framework

Youngwoo Koh; Sanghyuk Lee; Ryo Takada

doi:10.1016/j.jde.2013.09.017

Strichartz estimates for the Euler equations in the rotational framework

Youngwoo Koh, Sanghyuk Lee, Ryo Takada

SCI - Mathematics

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

18 Citations (Scopus)

Abstract

We consider the initial value problems of the incompressible Euler equations in the rotational framework. We obtain the optimal range of the Strichartz estimate for the linear group associated with the Coriolis forces. As an application, we prove that the lifespan of the solution can be taken arbitrarily large provided that the speed of rotation is sufficiently high.

Original language	English
Pages (from-to)	707-744
Number of pages	38
Journal	Journal of Differential Equations
Volume	256
Issue number	2
DOIs	https://doi.org/10.1016/j.jde.2013.09.017
Publication status	Published - 2014 Jan 15

Keywords

Coriolis force
Euler equations
Strichartz estimates

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.jde.2013.09.017

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title = "Strichartz estimates for the Euler equations in the rotational framework",

abstract = "We consider the initial value problems of the incompressible Euler equations in the rotational framework. We obtain the optimal range of the Strichartz estimate for the linear group associated with the Coriolis forces. As an application, we prove that the lifespan of the solution can be taken arbitrarily large provided that the speed of rotation is sufficiently high.",

keywords = "Coriolis force, Euler equations, Strichartz estimates",

author = "Youngwoo Koh and Sanghyuk Lee and Ryo Takada",

note = "Funding Information: Y. Koh is supported by NRF Grant 2012008373 (Korea) and S. Lee is supported in part by NRF Grant 20120000940 (Korea). R. Takada was supported by JSPS Research Fellowships for Young Scientists and partly supported by the JSPS Institutional Program for Young Researcher Overseas Visits “Promoting international young researchers in mathematics and mathematical sciences led by OCAMI”.",

year = "2014",

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doi = "10.1016/j.jde.2013.09.017",

language = "English",

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journal = "Journal of Differential Equations",

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T1 - Strichartz estimates for the Euler equations in the rotational framework

AU - Koh, Youngwoo

AU - Lee, Sanghyuk

AU - Takada, Ryo

N1 - Funding Information: Y. Koh is supported by NRF Grant 2012008373 (Korea) and S. Lee is supported in part by NRF Grant 20120000940 (Korea). R. Takada was supported by JSPS Research Fellowships for Young Scientists and partly supported by the JSPS Institutional Program for Young Researcher Overseas Visits “Promoting international young researchers in mathematics and mathematical sciences led by OCAMI”.

PY - 2014/1/15

Y1 - 2014/1/15

N2 - We consider the initial value problems of the incompressible Euler equations in the rotational framework. We obtain the optimal range of the Strichartz estimate for the linear group associated with the Coriolis forces. As an application, we prove that the lifespan of the solution can be taken arbitrarily large provided that the speed of rotation is sufficiently high.

AB - We consider the initial value problems of the incompressible Euler equations in the rotational framework. We obtain the optimal range of the Strichartz estimate for the linear group associated with the Coriolis forces. As an application, we prove that the lifespan of the solution can be taken arbitrarily large provided that the speed of rotation is sufficiently high.

KW - Coriolis force

KW - Euler equations

KW - Strichartz estimates

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M3 - Article

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VL - 256

SP - 707

EP - 744

JO - Journal of Differential Equations

JF - Journal of Differential Equations

SN - 0022-0396

IS - 2

ER -

Strichartz estimates for the Euler equations in the rotational framework

Abstract

Keywords

ASJC Scopus subject areas

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