Local and global existence results for the Navier-Stokes equations in the rotational framework

Daoyuan Fang; Bin Han; Matthias Georg Hieber

doi:10.3934/cpaa.2015.14.609

Local and global existence results for the Navier-Stokes equations in the rotational framework

Daoyuan Fang, Bin Han, Matthias Georg Hieber

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

6 Citations (Scopus)

Abstract

Consider the equations of Navier-Stokes in R³ in the rotational setting, i.e. with Coriolis force. It is shown that this set of equations admits a unique, global mild solution provided only the horizontal components of the initial data are small with respect to the norm the Fourier-Besov space {equation presented} (R³), where p ∈ [2,∞] and r∈ [1,∞).

Original language	English
Pages (from-to)	609-622
Number of pages	14
Journal	Communications on Pure and Applied Analysis
Volume	14
Issue number	2
DOIs	https://doi.org/10.3934/cpaa.2015.14.609
Publication status	Published - 2015 Mar 1
Externally published	Yes

Keywords

Chemin-Lerner space
Fourier-Besov space
Global solution
Littlewood- Paley decomposition
Rotational ows

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.3934/cpaa.2015.14.609

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abstract = "Consider the equations of Navier-Stokes in R3 in the rotational setting, i.e. with Coriolis force. It is shown that this set of equations admits a unique, global mild solution provided only the horizontal components of the initial data are small with respect to the norm the Fourier-Besov space {equation presented} (R3), where p ∈ [2,∞] and r∈ [1,∞).",

keywords = "Chemin-Lerner space, Fourier-Besov space, Global solution, Littlewood- Paley decomposition, Rotational ows",

author = "Daoyuan Fang and Bin Han and Hieber, {Matthias Georg}",

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journal = "Communications on Pure and Applied Analysis",

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T1 - Local and global existence results for the Navier-Stokes equations in the rotational framework

AU - Fang, Daoyuan

AU - Han, Bin

AU - Hieber, Matthias Georg

PY - 2015/3/1

Y1 - 2015/3/1

N2 - Consider the equations of Navier-Stokes in R3 in the rotational setting, i.e. with Coriolis force. It is shown that this set of equations admits a unique, global mild solution provided only the horizontal components of the initial data are small with respect to the norm the Fourier-Besov space {equation presented} (R3), where p ∈ [2,∞] and r∈ [1,∞).

AB - Consider the equations of Navier-Stokes in R3 in the rotational setting, i.e. with Coriolis force. It is shown that this set of equations admits a unique, global mild solution provided only the horizontal components of the initial data are small with respect to the norm the Fourier-Besov space {equation presented} (R3), where p ∈ [2,∞] and r∈ [1,∞).

KW - Chemin-Lerner space

KW - Fourier-Besov space

KW - Global solution

KW - Littlewood- Paley decomposition

KW - Rotational ows

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SP - 609

EP - 622

JO - Communications on Pure and Applied Analysis

JF - Communications on Pure and Applied Analysis

IS - 2

ER -

Local and global existence results for the Navier-Stokes equations in the rotational framework

Abstract

Keywords

ASJC Scopus subject areas

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