L p-theory of the Navier-Stokes flow in the exterior of a moving or rotating obstacle

Matthias Geissert; Horst Heck; Matthias Georg Hieber

doi:10.1515/CRELLE.2006.051

L p-theory of the Navier-Stokes flow in the exterior of a moving or rotating obstacle

Matthias Geissert^*, Horst Heck, Matthias Georg Hieber

^*Corresponding author for this work

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

74 Citations (Scopus)

Abstract

Consider the equations of Navier-Stokes in the exterior of a rotating domain. It is shown that, after rewriting the problem on a fixed domain Ω, the solution of the corresponding Stokes equation is governed by a C ₀-semigroup on L _σ ^p(Ω), 1 <p <∞, with generator . Moreover, for and initial data u ₀ ∈ L _σ ^p(Ω), we prove the existence of a unique local mild solution to the Navier-Stokes problem.

Original language	English
Pages (from-to)	45-62
Number of pages	18
Journal	Journal fur die Reine und Angewandte Mathematik
Issue number	596
DOIs	https://doi.org/10.1515/CRELLE.2006.051
Publication status	Published - 2006 Jul 1
Externally published	Yes

ASJC Scopus subject areas

Mathematics(all)

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abstract = "Consider the equations of Navier-Stokes in the exterior of a rotating domain. It is shown that, after rewriting the problem on a fixed domain Ω, the solution of the corresponding Stokes equation is governed by a C 0-semigroup on L σ p(Ω), 1 0 ∈ L σ p(Ω), we prove the existence of a unique local mild solution to the Navier-Stokes problem.",

author = "Matthias Geissert and Horst Heck and Hieber, {Matthias Georg}",

year = "2006",

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AU - Heck, Horst

AU - Hieber, Matthias Georg

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N2 - Consider the equations of Navier-Stokes in the exterior of a rotating domain. It is shown that, after rewriting the problem on a fixed domain Ω, the solution of the corresponding Stokes equation is governed by a C 0-semigroup on L σ p(Ω), 1 0 ∈ L σ p(Ω), we prove the existence of a unique local mild solution to the Navier-Stokes problem.

AB - Consider the equations of Navier-Stokes in the exterior of a rotating domain. It is shown that, after rewriting the problem on a fixed domain Ω, the solution of the corresponding Stokes equation is governed by a C 0-semigroup on L σ p(Ω), 1 0 ∈ L σ p(Ω), we prove the existence of a unique local mild solution to the Navier-Stokes problem.

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L p-theory of the Navier-Stokes flow in the exterior of a moving or rotating obstacle

Abstract

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