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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
##### Keywords:
uniqueness; mild solution
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##### References:
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