A functional central limit theorem for transformed solutions of the multidimensional Burgers equation with random initial data. (Q1432297)

The author considers the multidimensional Burgers equation with random initial data as a random field. This equation and its analogues describe various nonlinear physical processes, such as acoustic and intensive optical waves, turbulent phenomena, hydrodynamic flows of particles, etc. The main result of the paper is to prove the weak convergence of the distributions of the random fields \(V_T(t,x):=T^{{d}/{4}+{1}/{2}}v(tT,x\sqrt{T})\) to the distribution of a Gaussian field as \(T\to+\infty,\) where \(v\) is the solution of the Burgers equation, \(x\in R^d\), \(d>1\), \(t\in R_+.\) The author obtains a new maximum and moment inequalities for random fields to prove this main result.