The law of the iterated logarithm for the solution of the Burgers equation with random initial data

The law of the iterated logarithm is established for the solution of the one-dimensional Burgers equation in the case where the initial potential is described by a zero-range shot noise.Translated fromMatematicheskie Zametki, Vol. 64, No. 6, pp. 812–823, December, 1998.The author wishes to thank Professor A. V. Bulinskii for setting the problem and for his attention to the work on the paper.