The Navier-Stokes flow in the exterior of rotating obstacles

Research output: Chapter in Book/Report/Conference proceedingChapter

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 ∈ 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.

Original languageEnglish
Title of host publicationProgress in Nonlinear Differential Equations and Their Application
PublisherSpringer US
Pages243-250
Number of pages8
DOIs
Publication statusPublished - 2005 Jan 1
Externally publishedYes

Publication series

NameProgress in Nonlinear Differential Equations and Their Application
Volume64
ISSN (Print)1421-1750
ISSN (Electronic)2374-0280

Fingerprint

Mild Solution
Stokes Flow
Navier-Stokes
Rotating
Navier-Stokes Problem
Compatibility Conditions
Exterior Domain
Rewriting

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

Cite this

Hieber, M. G. (2005). The Navier-Stokes flow in the exterior of rotating obstacles. In Progress in Nonlinear Differential Equations and Their Application (pp. 243-250). (Progress in Nonlinear Differential Equations and Their Application; Vol. 64). Springer US. https://doi.org/10.1007/3-7643-7385-7_13

The Navier-Stokes flow in the exterior of rotating obstacles. / Hieber, Matthias Georg.

Progress in Nonlinear Differential Equations and Their Application. Springer US, 2005. p. 243-250 (Progress in Nonlinear Differential Equations and Their Application; Vol. 64).

Research output: Chapter in Book/Report/Conference proceedingChapter

Hieber, MG 2005, The Navier-Stokes flow in the exterior of rotating obstacles. in Progress in Nonlinear Differential Equations and Their Application. Progress in Nonlinear Differential Equations and Their Application, vol. 64, Springer US, pp. 243-250. https://doi.org/10.1007/3-7643-7385-7_13
Hieber MG. The Navier-Stokes flow in the exterior of rotating obstacles. In Progress in Nonlinear Differential Equations and Their Application. Springer US. 2005. p. 243-250. (Progress in Nonlinear Differential Equations and Their Application). https://doi.org/10.1007/3-7643-7385-7_13
Hieber, Matthias Georg. / The Navier-Stokes flow in the exterior of rotating obstacles. Progress in Nonlinear Differential Equations and Their Application. Springer US, 2005. pp. 243-250 (Progress in Nonlinear Differential Equations and Their Application).
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