The Navier-Stokes flow in the exterior of rotating obstacles

Matthias Georg Hieber

doi:10.1007/3-7643-7385-7_13

The Navier-Stokes flow in the exterior of rotating obstacles

Matthias Georg Hieber^*

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Chapter

Abstract

In this note we describe recent results on the equations of Navier-Stokes in the exterior of a rotating domain. After rewriting the problem on a fixed exterior domain Ω in ℝⁿ, it is shown that for initial data u₀ ∈ L_σ ^p (Ω) with p ≥ n and which are satisfying a certain compatibility condition there exists a unique local mild solution to the Navier-Stokes problem. In the case of the whole space of ℝⁿ, this local mild solution is even analytic in the space variable x.

Original language	English
Title of host publication	Progress in Nonlinear Differential Equations and Their Application
Publisher	Springer US
Pages	243-250
Number of pages	8
DOIs	https://doi.org/10.1007/3-7643-7385-7_13
Publication status	Published - 2005 Jan 1
Externally published	Yes

Publication series

Name	Progress in Nonlinear Differential Equations and Their Application
Volume	64
ISSN (Print)	1421-1750
ISSN (Electronic)	2374-0280

Keywords

Exterior domain
Local existence
Mild solution
Stokes operator
Weak solution

ASJC Scopus subject areas

Analysis
Applied Mathematics
Control and Optimization
Mathematical Physics
Computational Mechanics

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10.1007/3-7643-7385-7_13

Cite this

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AB - In this note we describe recent results on the equations of Navier-Stokes in the exterior of a rotating domain. After rewriting the problem on a fixed exterior domain Ω in ℝn, it is shown that for initial data u0 ∈ Lσ p (Ω) with p ≥ n and which are satisfying a certain compatibility condition there exists a unique local mild solution to the Navier-Stokes problem. In the case of the whole space of ℝn, this local mild solution is even analytic in the space variable x.

KW - Exterior domain

KW - Local existence

KW - Mild solution

KW - Stokes operator

KW - Weak solution

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BT - Progress in Nonlinear Differential Equations and Their Application

PB - Springer US

ER -

The Navier-Stokes flow in the exterior of rotating obstacles

Abstract

Publication series

Keywords

ASJC Scopus subject areas

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