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Article Contents

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

• 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.
Mathematics Subject Classification: Primary: 35Q30, 76D; Secondary: 76M.

 Citation:

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