Abstract：

 

This is the second part of the same topic which we began to discuss in May 13. Recall that it is still a long standing open problem to decide whether or not there are any non-trivial, non-constant bounded ancient mild solutions to the Navier-Stokes equation in the setting of 3D-Euclidean space. This time, we will talk about some partial results about the Louville's conjecture in the case of axi-symmetric 3D Navier-Stokes flows.