A dispersive estimate for the multidimensional Burgers equation

We study the multi-dimensional Burgers equation $u_t + u u_{x_1} + \dots + u^d u_{x_d} = 0$\mathrm{.}Weprovethatthe$L^\infty$ norm of entropy solutions of this equation decays polynomially as $t\to \mathrm{\infty }$ in terms of the $L^1$ norm of the initial data only.