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A General Approach to Time Periodic Incompressible Viscous Fluid Flow Problems

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Abstract

This article develops a general approach to time periodic incompressible fluid flow problems and semilinear evolution equations. It yields, on the one hand, a unified approach to various classical problems in incompressible fluid flow and, on the other hand, gives new results for periodic solutions to the Navier–Stokes–Oseen flow, the Navier–Stokes flow past rotating obstacles, and, in the geophysical setting, for Ornstein–Uhlenbeck and various diffusion equations with rough coefficients. The method is based on a combination of interpolation and topological arguments, as well as on the smoothing properties of the linearized equation.

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Authors and Affiliations

  1. Fachbereich Mathematik, TU Darmstadt, Schlossgartenstr. 7, 64289, Darmstadt, Germany

    Matthias Geissert & Matthias Hieber

  2. University of Pittsburgh, 607 Benedum Engineering Hall, Pittsburgh, PA, 15261, USA

    Matthias Hieber

  3. School of Applied Mathematics and Informatics, Hanoi University of Science and Technology, Vien Toan ung dung va Tin hoc, Dai hoc Bach khoa Hanoi, 1 Dai Co Viet, Hanoi, Vietnam

    Thieu Huy Nguyen

Authors
  1. Matthias Geissert
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  2. Matthias Hieber
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  3. Thieu Huy Nguyen
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Correspondence to Thieu Huy Nguyen.

Additional information

Communicated by E. G. Virga

Thieu Huy Nguyen, on leave from Hanoi University of Science and Technology as a research fellow of the Alexander von Humboldt Foundation.

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Geissert, M., Hieber, M. & Nguyen, T.H. A General Approach to Time Periodic Incompressible Viscous Fluid Flow Problems. Arch Rational Mech Anal 220, 1095–1118 (2016). https://doi.org/10.1007/s00205-015-0949-8

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  • DOI: https://doi.org/10.1007/s00205-015-0949-8

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