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Erschienen in:
An Implicit Boundary Integral Method for Interfaces Evolving by Mullins-Sekerka Dynamics Kapitel lesen Erstes Kapitel lesen

2017 | OriginalPaper | Buchkapitel

On Periodic and Almost Periodic Solutions to Incompressible Viscous Fluid Flow Problems on the Whole Line

verfasst von : Matthias Hieber, Thieu Huy Nguyen, Anton Seyfert

Erschienen in: Mathematics for Nonlinear Phenomena — Analysis and Computation

Verlag: Springer International Publishing

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Abstract

It is shown that a large class of semilinear evolution equations on the whole line with periodic or almost periodic forces admit periodic or almost periodic mild solutions. The approach presented generalizes the method described in [28] to the case of the whole line and to forces which are almost periodic in the sense of H. Bohr. It relies on interpolation methods and on \(L^p-L^q\)-smoothing properties of the underlying linearized equation. Applied to incompressible fluid flow problems, the approach yields new results on (almost) periodic solutions to the Navier-Stokes-Oseen equations, to the flow past rotating obstacles, to the Navier-Stokes equations in the rotational setting as well as to Ornstein–Uhlenbeck type equations.

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Vorheriges Kapitel A Note on Regularity Criteria for Navier-Stokes System
Nächstes Kapitel Remarks on Viscosity Solutions for Mean Curvature Flow with Obstacles
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Metadaten
Titel
On Periodic and Almost Periodic Solutions to Incompressible Viscous Fluid Flow Problems on the Whole Line
verfasst von
Matthias Hieber
Thieu Huy Nguyen
Anton Seyfert
Copyright-Jahr
2017
Buch
Mathematics for Nonlinear Phenomena — Analysis and Computation

Print ISBN: 978-3-319-66762-1

Electronic ISBN: 978-3-319-66764-5

Copyright-Jahr: 2017

DOI
https://doi.org/10.1007/978-3-319-66764-5_4