  In this paper we deal with local estimates for parabolic problems in
$\mathbb{R}^N$ with absorbing first order terms, whose model is $\{ {l} u_t-
\Delta u +u |\nabla u|^q = f(t,x) \quad &{in}\, (0,T) \times \mathbb{R}^N\,,
\\[1.5 ex] u(0,x)= u_0 (x) &box{in}\, \mathbb{R}^N.$ where $T>0$, $N\geq 2$,
$1<q\leq 2$, $f(t,x)\in L^1( 0,T; L^1_{\rm loc} (\mathbb{R}^N))$ and $u_0\in
L^1_{\rm loc} (\mathbb{R}^N)$.
