  In this paper, we provide two-sided estimates and uniform asymptotics for the
solution of $d$-dimensional critical fractal Burgers equation
$u_t-\Delta^{\alpha/2}u+b\cdot \nabla\left(u|u|^q\right)=0$, $\alpha\in(1,2)$,
$b\in\mathbb R^d$ for $q = (\alpha-1)/d$ and $u_0 \in L^1(\mathbb R^d)$. We
consider also $q > (\alpha-1)/d$ under additional condition $u_0 \in
L^\infty(\mathbb R^d)$. In both cases we assume $u_0\geq0$, which implies that
the solution is non-negative. The estimates are given in the terms of the
function $P_t u_0$, where $P_t$ is the stable semigroup operator.
