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Asymptotic properties of steady solutions to the 3D axisymmetric Navier-Stokes equations with no swirl. (English) Zbl 1479.35620

Summary: We study the asymptotic behavior of axisymmetric solutions with no swirl to the steady Navier-Stokes equations in the outside of the cylinder. We prove an a priori decay estimate of the vorticity under the assumption that the velocity has generalized finite Dirichlet integral. As an application, we obtain a Liouville-type theorem.

MSC:

35Q30 Navier-Stokes equations
35B53 Liouville theorems and Phragmén-Lindelöf theorems in context of PDEs
35B40 Asymptotic behavior of solutions to PDEs
35B45 A priori estimates in context of PDEs
76D05 Navier-Stokes equations for incompressible viscous fluids
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