PDE Seminar (2016/10/21): Global well-posedness of the two-dimensional exterior Navier-Stokes equations for non-decaying data, Ken Abe (Kyoto University)

2016-10-21 16:30 - 2016-10-21 17:30
Faculty of Science Building #3, Room 309
Ken Abe (Kyoto University)
We consider the two-dimensional Navier-Stokes equations in an exterior domain, subject to the non-slip boundary condition. It is well known that there exist various non-trivial stationary solutions, which are asymptotically constant and with a finite Dirichlet integral. On the other hand, even local solvability was unknown for the non-stationary problem for such non-decaying initial data. In this talk, we report some global well-posedness result for bounded initial data with a finite Dirichlet integral, and existence of asymptotically constant solutions for arbitrary large Reynolds numbers.