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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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