Partial Differential Equations and Applied Mathematics Seminar
Date/Time: March 15th, Tue., 5:00 ~ 6:00 PM
Location: Science Building #225 Yonsei University
Speaker: Prof. Ken Abe
Affiliation: Kyoto University, Japan
Title: Global well-posedness of the axisymmetric Navier-Stokes equations in the exterior of an infinite cylinder
We consider the initial-boundary value problem of the Navier-Stokes equations for axisymmetric initial data with swirl in the exterior of an infinite cylinder, subject to the slip boundary condition. We construct global solutions and estimate potential singularities of axisymmetric flows in the whole space by using the size of the cylinder. The proof is based on the Boussinesq system. We show that the system is globally well-posed in the exterior domain for axisymmetric initial data without swirl.