Global solutions for the Navier-Stokes equations in the rotational framework

Tsukasa Iwabuchi; Ryo Takada

doi:10.1007/s00208-013-0923-4

Global solutions for the Navier-Stokes equations in the rotational framework

Tsukasa Iwabuchi
, Ryo Takada

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

61 Citations (Scopus)

Abstract

The existence of global unique solutions to the Navier-Stokes equations with the Coriolis force is established in the homogeneous Sobolev spaces H^s (ℝ³)³ for 1/2 < s < 3/4 if the speed of rotation is sufficiently large. This phenomenon is so-called the global regularity. The relationship between the size of initial datum and the speed of rotation is also derived. The proof is based on the space time estimates of the Strichartz type for the semigroup associated with the linearized equations. In the scaling critical space H^1/2(ℝ³)³, the global regularity is also shown.

Original language	English
Pages (from-to)	727-741
Number of pages	15
Journal	Mathematische Annalen
Volume	357
Issue number	2
DOIs	https://doi.org/10.1007/s00208-013-0923-4
Publication status	Published - Oct 2013
Externally published	Yes

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1007/s00208-013-0923-4

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title = "Global solutions for the Navier-Stokes equations in the rotational framework",

abstract = "The existence of global unique solutions to the Navier-Stokes equations with the Coriolis force is established in the homogeneous Sobolev spaces Hs (ℝ3)3 for 1/2 < s < 3/4 if the speed of rotation is sufficiently large. This phenomenon is so-called the global regularity. The relationship between the size of initial datum and the speed of rotation is also derived. The proof is based on the space time estimates of the Strichartz type for the semigroup associated with the linearized equations. In the scaling critical space H1/2(ℝ3)3, the global regularity is also shown.",

author = "Tsukasa Iwabuchi and Ryo Takada",

note = "Funding Information: The authors would like to express his great thanks to Professor Hideo Kozono for his valuable advices and continuous encouragement. The authors would like to thank the referee for his constructive suggestions. The second author is partly supported by Research Fellow of the Japan Society for the Promotion of Science for Young Scientists.",

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language = "English",

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TY - JOUR

T1 - Global solutions for the Navier-Stokes equations in the rotational framework

AU - Iwabuchi, Tsukasa

AU - Takada, Ryo

N1 - Funding Information: The authors would like to express his great thanks to Professor Hideo Kozono for his valuable advices and continuous encouragement. The authors would like to thank the referee for his constructive suggestions. The second author is partly supported by Research Fellow of the Japan Society for the Promotion of Science for Young Scientists.

PY - 2013/10

Y1 - 2013/10

N2 - The existence of global unique solutions to the Navier-Stokes equations with the Coriolis force is established in the homogeneous Sobolev spaces Hs (ℝ3)3 for 1/2 < s < 3/4 if the speed of rotation is sufficiently large. This phenomenon is so-called the global regularity. The relationship between the size of initial datum and the speed of rotation is also derived. The proof is based on the space time estimates of the Strichartz type for the semigroup associated with the linearized equations. In the scaling critical space H1/2(ℝ3)3, the global regularity is also shown.

AB - The existence of global unique solutions to the Navier-Stokes equations with the Coriolis force is established in the homogeneous Sobolev spaces Hs (ℝ3)3 for 1/2 < s < 3/4 if the speed of rotation is sufficiently large. This phenomenon is so-called the global regularity. The relationship between the size of initial datum and the speed of rotation is also derived. The proof is based on the space time estimates of the Strichartz type for the semigroup associated with the linearized equations. In the scaling critical space H1/2(ℝ3)3, the global regularity is also shown.

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DO - 10.1007/s00208-013-0923-4

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JO - Mathematische Annalen

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ER -

Global solutions for the Navier-Stokes equations in the rotational framework

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