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in classical mathematical physics
The time-periodic solutions of the Navier-Stokes equations with mixed boundary conditions
In this paper we deal with the system of
periodic Navier-Stokes equations with mixed boundary conditions. We
define Banach spaces XP and
YP, respectively, the space of
"possible'' solutions of this problem and the space of its data. We
define the operator NP : Xp $\to$ YP and formulate our problem in
terms of operator equations. Let u $\in$ XP and gP u : XP $\to$ YP
be the Frechet derivative of NP atu . Denote by MR the
set of all functions u such that gPu is one-to-one and onto
YP . We prove that MR is weakly dense and weakly open.