| Abstract: |
| We consider the three-dimensional Navier-Stokes equations for axisymmetric initial data.
It is known that the Cauchy problem is globally well-posed for large axisymmetric
initial data in L_3 with finite energy, if the swirl component of initial velocity is identically
zero (with no swirl). However, unique solvability is unknown in general for the case with swirl.
In this talk, we study axisymmetric flows with swirl in the exterior of an infinite cylinder subject to
the slip boundary condition. We report unique existence of global solutions for large
axisymmetric data in L_3 with finite energy, satisfying a decay condition of the swirl
component. |
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