A blowup criteria along maximum points of the 3D-Navier-Stokes flow in   terms of function spaces with variable growth condition
  A blowup criteria along maximum point of the 3D-Navier-Stokes flow in terms of function spaces with variable growth condition is constructed. This criterion is different from the Beale-Kato-Majda type and Constantin-Fefferman type criterion. If geometric behavior of the velocity vector field near the maximum point has a kind of symmetry up to a possible blowup time, then the solution can be extended to be the strong solution beyond the possible blowup time. 
Eiichi Nakai and Tsuyoshi Yoneda
math.AP