Hu, Yiming et A. Woyczynski, W., An Extremal Rearrangement Property of Statistical Solutions of Burgers' Equation, Annals of applied probability , 4(3), 1994, pp. 838-858
We prove that a certain (centered unimodal) rearrangement of coefficients in the moving average initial input process maximizes the variance (energy density) of the limit distribution of the spatiotemporal random field solution of a nonlinear partial differential equation called Burgers' equation. Our proof is in the spirit of domination principles developed in the book by Kwapien and Woyczynski.