LARGE-DEVIATION ANALYSIS OF BURGERS TURBULENCE WITH WHITE-NOISE INITIAL DATA

The statistics of the solution to the inviscid Burgers equation are in vestigated when the initial velocity is a white-noise function. Explic it representations for the probability distribution functions (PDFs) o f the velocity and the distance between two successive shocks are foun d in terms of the solution to a PDE system. By using these expressions and large-deviation theory, tight bounds are found for the tails of t hese distributions and for that of the shock-strength distribution. Th ese bounds give the exact rates of decay for the tails. (C) 1998 John Wiley & Sons, Inc.