NCKU Math Colloquium

DATE2016-03-10 16:10-17:00



TITLEAsymptotic Properties of Stationary Navier-Stokes Flows in the Setting of Hyperbolic Spaces

ABSTRACT In this talk, I will present a piece of recent joint work with Che-Kai Chen and Magdalena Czubak. In this work, we consider a stationary Navier-Stokes flow which passes a circular-shape obstacle in a 2-dimensional hyperbolic space. We suppose that the stationary Navier-Stokes flow under our consideration satisfies the finite Dirichlet-norm property. Under this assumption alone, we show that the velocity field itself will decay to zero at infinity, and that we can obtain an exponential decay of the associated vorticity of the flow in the far range. The material which will be reported in this talk is a preliminary version of a piece of unpublished recent joint work with Che-Kai Chen and Magdalena Czubak. During the talk, we will also mention the relations between this piece of work with the standard working knowledge in the classical theory of stationary Navier-Stokes flows passing an obstacle in the 2D Euclidean setting. In the meanwhile, I will also mention my previous joint research works with my friend professor Magdalena Czubak about our studies of global analytic properties of Navier-Stokes flows in the hyperbolic setting.