On a Pump
Tóm tắt
We examine the Navier–Stokes equations in a two space dimensional time dependent domain. The system is considered with nonhomogeneous slip boundary conditions. The main result shows that under a certain geometrical constraint on deformations of the domain, it is possible to prove existence of solutions globally in time for arbitrary flows across the boundary with a new time independent bound on the vorticity. The geometrical restriction does not imply simply connectedness of the domain. Our model may be treated as a simple model of a pump.
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