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Vanishing viscosity limit for incompressible flow inside a rotating circle. (English) Zbl 1143.76416

Summary: We consider circularly symmetric incompressible viscous flow in a disk. The boundary condition is no-slip with respect to a prescribed time-dependent rotation of the boundary about the center of the disk. We prove that, if the prescribed angular velocity of the boundary has finite total variation, then the Navier-Stokes solutions converge strongly in \(L^{2}\) to the corresponding stationary solution of the Euler equations when viscosity vanishes. Our approach is based on a semigroup treatment of the symmetry-reduced scalar equation.

MSC:

76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids
76U05 General theory of rotating fluids
35Q30 Navier-Stokes equations
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