## On the Navier-Stokes Equations in Time Dependent Domains and with Boundary Conditions Involving the Pressure

J. Math. Sci. Univ. Tokyo
Vol. 4 (1997), No. 3, Page 529--550.

Åukaszewicz, Grzegorz
On the Navier-Stokes Equations in Time Dependent Domains and with Boundary Conditions Involving the Pressure
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Abstract:
We present a weak formulation of an initial boundary value problem for the Navier-Stokes equations in domains with moving boundaries. The boundary conditions are nonstandard. In general, the boundary consists of three hypersurfaces $\G_1$, $\G_2$ and $\G_3$. On $\G_1$ and $\G_3$ the velocity field and the normal component of the velocity field are posed, respectively, while on $\G_2$ the dynamic pressure is given. Under suitable complementary conditions we prove existence of weak solutions to the considered problem and give examples of its applications including, in particular, flows through pipes and in bearings.

Mathematics Subject Classification (1991): 35Q30, 76D05
Mathematical Reviews Number: MR1484601