Stationary solutions of the two-dimensional Navier-Stokes exterior problem

Date
2015/06/26 Fri 16:45 - 17:45
Room
3号館251号室
Speaker
山崎 昌男
Affiliation
早稲田大学理工学術院
Abstract

We are concerned with the stationary solutions vanishing at infinity of the boundary value problem of the Navier-Stokes equations with nonzero external forces and boundary data. We first show the existence under assumptions more general than in the previous works, and show that the weak solutions satisfy the energy inequality for nonzero boundary data. Then we show that, if there exists a small nontrivial solution with sufficient decay, then every weak solution satisfying the energy inequality must coincide with the aforementioned solution with sufficient decay. Finally we show that the solution with sufficient decay do exist under a new symmetry condition on the external force and boundary data.