Long time existence of classical solutions for the 3D incompressible rotating Euler equations

Ryo Takada

doi:10.2969/jmsj/06820579

Long time existence of classical solutions for the 3D incompressible rotating Euler equations

Ryo Takada

SCI - Mathematics

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

9 Citations (Scopus)

Abstract

We consider the initial value problem of the 3D incompressible rotating Euler equations. We prove the long time existence of classical solutions for initial data in H^s(ℝ³) with s > 5/2. Also, we give an upper bound of the minimum speed of rotation for the long time existence when initial data belong to H^7/2(ℝ³).

Original language	English
Pages (from-to)	579-608
Number of pages	30
Journal	Journal of the Mathematical Society of Japan
Volume	68
Issue number	2
DOIs	https://doi.org/10.2969/jmsj/06820579
Publication status	Published - 2016

Keywords

Long time existence
The 3D Euler equations
The Coriolis force

ASJC Scopus subject areas

Mathematics(all)

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10.2969/jmsj/06820579

Cite this

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title = "Long time existence of classical solutions for the 3D incompressible rotating Euler equations",

abstract = "We consider the initial value problem of the 3D incompressible rotating Euler equations. We prove the long time existence of classical solutions for initial data in Hs(ℝ3) with s > 5/2. Also, we give an upper bound of the minimum speed of rotation for the long time existence when initial data belong to H7/2(ℝ3).",

keywords = "Long time existence, The 3D Euler equations, The Coriolis force",

author = "Ryo Takada",

note = "Funding Information: This work was supported by JSPS Grant-in-Aid for Research Activity Start-up Grant Number 25887005. Publisher Copyright: {\textcopyright} 2016 The Mathematical Society of Japan.",

year = "2016",

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language = "English",

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AB - We consider the initial value problem of the 3D incompressible rotating Euler equations. We prove the long time existence of classical solutions for initial data in Hs(ℝ3) with s > 5/2. Also, we give an upper bound of the minimum speed of rotation for the long time existence when initial data belong to H7/2(ℝ3).

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KW - The 3D Euler equations

KW - The Coriolis force

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Long time existence of classical solutions for the 3D incompressible rotating Euler equations

Abstract

Keywords

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