A dispersive estimate for the multidimensional Burgers equation

Abstract

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

References in corpus (1)

• Multi-dimensional scalar conservation laws with unbounded integrable initial data

Cited by in corpus (1)

• Multi-dimensional Burgers equation with unbounded initial data: well-posedness and dispersive estimates