| 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. |
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