HAUSDORFF DIMENSION OF REGULAR POINTS IN STOCHASTIC BURGERS FLOWS WITH LEVY ALPHA-STABLE INITIAL DATA

This paper studies statistical properties of shocks for the inviscid B urgers equation with an alpha-stable Levy motion initial data. In the absence of analytic results, numerical and computer simulation tools a re utilized. Qualitative and quantitative information on the scaling p roperties of Lagrangian regular points of solutions is obtained and, i n particular, their Hausdorff dimension is estimated to be 1/alpha. Th is suggests a possible extension of Ya. Sinai's result for Brownian in itial data.