Discrete and Continuous Dynamical Systems - Series S (DCDS-S)

Existence and uniqueness of time-periodic solutions to the Navier-Stokes equations in the whole plane

Pages: 1237 - 1257, Volume 6, Issue 5, October 2013      doi:10.3934/dcdss.2013.6.1237

       Abstract        References        Full Text (511.1K)       Related Articles       

Giovanni P. Galdi - Department of Mechanical Engineering and Materials Science, University of Pittsburgh, Pittsburgh, PA 15261, United States (email)

Abstract: We consider the two-dimensional motion of a Navier-Stokes liquid in the whole plane, under the action of a time-periodic body force $F$ of period $T$, and tending to a prescribed nonzero constant velocity at infinity. We show that if the magnitude of $F$, in suitable norm, is sufficiently small, there exists one and only one corresponding time-periodic flow of period $T$ in an appropriate function class.

Keywords:  Navier-Stokes equations, time-periodic solutions, plane flow.
Mathematics Subject Classification:  Primary: 35Q30, 76D; Secondary: 76M.

Received: November 2011;      Revised: February 2012;      Available Online: March 2013.