The inviscid Burgers equation with fractional Brownian initial data: the   dimension of regular Lagrangian points
  Fractional Brownian motion, H-FBM , of index 0<H<1 is considered as initial velocity in the inviscid Burgers equation. It is shown that the Hausdorff dimension of regular Lagrangian points at any moment t is equal to H. This fact validates the Sinai-Frisch conjecture known since 1992. 
G. Molchan
math-ph math.MP