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Strong solutions to the Navier-Stokes equations around a rotating obstacle. (English) Zbl 1081.35076
Summary: We study the existence of strong solutions to the three-dimensional Navier-Stokes initial-boundary value problem in the domain $$\Omega$$, exterior to a rigid body that rotates with constant angular velocity $$\omega$$. We show that when the initial data $$u_0$$, are prescribed in an appropriate functional class, a strong solution exists at least in some finite time interval. Moreover, the solution exists for all times, provided $$u_0$$, in suitable norm, and the magnitude of $$\omega$$ do not exceed a certain constant depending only on the kinematic viscosity and on the regularity of $$\Omega$$. In this latter case, we also show that the velocity field converges to the velocity field of the corresponding steady-state solution.

##### MSC:
 35Q30 Navier-Stokes equations 76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids 76U05 General theory of rotating fluids 35B45 A priori estimates in context of PDEs
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