ON HAUSDORFF DIMENSION OF BLOW-UP TIMES RELEVANT TO WEAK SOLUTION OF GENERALIZED NAVIER-STOKES FLUIDS

Abstract

We study qualitative properties of spatially periodic weak solutions to generalized Navier-Stokes fluids (of power-law type), which are known to exist for large data and arbitrary time intervals, in the case where the weak solution itself is not an admissible test function. We focus on establishing the upper estimates on the Hausdorff dimension of the possible times at which the L2-norm of the velocity gradient can blow up.

Keywords

• Husdorf dimension
• blow-up times
• Navier-Stokes equations