Special Session 77: Analysis and Applications of Nonlinear Elliptic and Parabolic Equations

Decay and vanishing of some D-solutions of the Navier-Stokes equations

Qi S Zhang
UC Riverside
USA
Co-Author(s):    B. Carrillo, X.H. Pan and Na Zhao
Abstract:
An old problem since Leray asks whether homogeneous D solutions of the 3 dimensional Navier-Stokes equation in or some noncompact domains such as R^3 or a slab are 0. In this paper, we give a positive solution to the problem in two special cases: (1) when the solution is axially symmetric and periodic in the vertical variable; (2) full 3 dimensional slab case with Dirichlet boundary condition. Other partial results will also be discussed. This is joint work with B. Carrillo, X.H. Pan and Na Zhao.