  We show existence of global strong solutions with large initial data on the
irrotational part for the shallow-water system in dimension $N\geq 2$. We
introduce a new notion of \textit{quasi-solutions} when the initial velocity is
assumed to be irrotational, these last one exhibit regularizing effects both on
the velocity and in a very surprising way also on the density (indeed the
density is a priori governed by an hyperbolic equation). We would like to point
out that this smoothing effect is purely non linear and is absolutely crucial
in order to deal with the pressure term as it provides new damping effects in
high frequencies. In particular our result gives a first kind of answer to the
problem of the existence of global weak solution for the shallow-water system.
We conclude by giving new point wise decay estimates on the solution which
improves the previous works \cite{HZ1,HZ2}.
