分野別セミナー

We consider the three-dimensional Navier-Stokes equations for axisymmetric initial data. It is well known that the Cauchy problem is globally well-posed for large axisymmetric initial data if the azimuthal component of initial velocity is identically zero (with no swirl). However, regularity and uniqueness is unknown in general for solutions with non-trivial swirls. In this talk, we study axisymmetric flows in the exterior of a cylinder subject to the slip boundary condition. We show that unique global-in-time solutions exist for large axisymmetric data in L_3 with finite energy satisfying a decay condition of the swirl component. This talk is based on a joint work with G. Seregin (University of Oxford).


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