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Time-Periodic Solutions to the Navier-Stokes Equations

In: Handbook of Mathematical Analysis in Mechanics of Viscous Fluids

Author

Listed:
  • Giovanni P. Galdi

    (University of Pittsburgh, Department of Mechanical Engineering and Materials Science)

  • Mads Kyed

    (Technische Universität Darmstadt, Fachbereich Mathematik)

Abstract

The Navier-Stokes equations with time-periodic data are investigated with respect to solutions of the same period. In the physical terms, such a system models the flow of a viscous liquid under the influence of a time-periodic force. The three most relevant types of flow domains, from a physical point of view, are considered: a bounded domain, an exterior domain, and an infinite pipe. Methods to show existence of both weak and strong solutions are introduced. Moreover, questions regarding regularity, uniqueness, and asymptotic structure at spatial infinity of solutions are addressed.

Suggested Citation

  • Giovanni P. Galdi & Mads Kyed, 2018. "Time-Periodic Solutions to the Navier-Stokes Equations," Springer Books, in: Yoshikazu Giga & Antonín Novotný (ed.), Handbook of Mathematical Analysis in Mechanics of Viscous Fluids, chapter 10, pages 509-578, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-13344-7_10
    DOI: 10.1007/978-3-319-13344-7_10
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