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A blowup criteria along maximum point of the 3D-Navier-Stokes flow in termsof function spaces with variable growth condition is constructed. Thiscriterion is different from the Beale-Kato-Majda type and Constantin-Feffermantype criterion. If geometric behavior of the velocity vector field near themaximum point has a kind of symmetry up to a possible blowup time, then thesolution can be extended to be the strong solution beyond the possible blowuptime.

A blowup criteria along maximum points of the 3D-Navier-Stokes flow in terms of function spaces with variable growth condition