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1 results

  • 2 - Time-periodic flow of a viscous liquid past a body

  • Edited by Charles L. Fefferman, Princeton University, New Jersey, James C. Robinson, University of Warwick, José L. Rodrigo, University of Warwick
  • Book:
    Partial Differential Equations in Fluid Mechanics
    Published online:
    15 August 2019
    Print publication:
    27 September 2018, pp 20-49

  • Summary

    We investigate existence, uniqueness and regularity of time-periodic solutions to the Navier-Stokes equations governing the flow of a viscous liquid past a three-dimensional body moving with a time-periodic translational velocity. The net motion of the body over a full time-period is assumed to be non-zero. In this case, the appropriate linearization is the time-periodic Oseen system in a three-dimensional exterior domain. A priori L^q estimates are established for this linearization. Based on these "maximal regularity" estimates, existence and uniqueness of smooth solutions to the fully nonlinear Navier-Stokes problem is obtained by the contraction mapping principle.