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Strong \(L^p\)-solutions to the Navier-Stokes flow past moving obstacles: The case of several obstacles and time-dependent velocity. (English) Zbl 1156.76016
Summary: We consider the Navier-Stokes flow past several moving or rotating obstacles with possible time-dependent velocity. It is shown that, under suitable assumptions on the data, there exists a unique local strong solution in the \( L^p\)-\(L^q\)-setting for suitable \( p,q \in (1,\infty)\). Moreover, it is proved that this strong solution coincides with the known mild solution in the very weak sense.

MSC:
76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids
35Q30 Navier-Stokes equations
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