On the Maximum Enstrophy Growth in Burgers Equation

The regularity of solutions of the three-dimensional Navier-Stokes equation is controlled by the boundedness of the enstrophy ?. The best estimate available to-date for its rate of growth is d?/dt ? C?3, where C > 0, which was recently found to be sharp by Lu & Doering (2008). Applying straightforward time-integration to this instantaneous estimate leads to the possibility of loss of regularity in finite time, the so-called blow-up, and …