  In this paper we investigate the question of the existence of global weak
solution for the compressible Navier Stokes equations provided that the initial
momentum $\rho_0 u_0$ belongs to $\mbox{bmo}^{-1}(\mathbb{R}^N)$ with $N= 2,3$
and is radially symmetric. More precisely we deal with the so called viscous
shallow water system when the viscosity coefficients verify
$\mu(\rho)=\mu\rho$, $\lambda(\rho)=0$ with $\mu>0$. We prove then a equivalent
of the so called Koch-Tataru theorem for the compressible Navier-Stokes
equations. In addition we assume that the initial density $\rho_0$ is only
bounded in $L^\infty(\mathbb{R}^N)$, it allows us in particular to consider
initial density admitting shocks. Furthermore we show that if the coupling
between the density and the velocity is sufficiently strong, then the initial
density which admits initially shocks is instantaneously regularizing inasmuch
as the density becomes Lipschitz. This coupling is expressed via the regularity
of the so called effective velocity $v=u+2\mu\nabla\ln\rho$. In our case $v_0$
belongs to $L^2(\mathbb{R}^N)\cap L^\infty(\mathbb{R}^N)$, it is important to
point out that this choice on the initial data implies that we work in a
setting of infinite energy on the initial data $(\rho_0,u_0)$, it extends in
particular the results of \cite{V}. In a similar way, we consider also the case
of the dimension $N=1$ where the momentum $\rho_0 u_0$ belongs to
$bmo^{-1}(\mathbb{R})$ without any geometric restriction.\\ To finish we prove
the global existence of strong solution for large initial data provided that
the initial data are radially symmetric and sufficiently regular in dimension
$N=2,3$ for $\gamma$ law pressure.
