Shock statistics in higher-dimensional Burgers turbulence
  We conjecture the exact shock statistics in the inviscid decaying Burgers equation in D>1 dimensions, with a special class of correlated initial velocities, which reduce to Brownian for D=1. The prediction is based on a field-theory argument, and receives support from our numerical calculations. We find that, along any given direction, shocks sizes and locations are uncorrelated. 
Pierre Le Doussal, Alberto Rosso, Kay J\"org Wiese
cond-mat.stat-mech