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We consider Navier-Stokes equations for compressible viscous fluids in theone-dimensional case with general viscosity coefficients. We prove theexistence of global weak solution when the initial momentum $\rho_0 u_0$belongs to the set of the finite measure ${\cal M}(\mathbb{R})$ and when theinitial density $\rho_0$ is in the set of bounded variation functions$BV(\mathbb{R})$. In particular it allows to deal with initial momentum whichare Dirac masses and initial density which admit shocks. We can observe inparticular that this type of initial data have infinite energy. Furthermore weshow that if the coupling between the density and the velocity is sufficientlystrong then the initial density which admits initially shocks isinstantaneously regularized and becomes continuous. This coupling is expressedvia the regularity of the so called effective velocity$v=u+\frac{\mu(\rho)}{\rho^2}\partial_x \rho$ with $\mu(\rho)$ the viscositycoefficient. Inversely if the coupling between the initial density and theinitial velocity is too weak (typically $\rho_0 v_0\in{\cal M}(\mathbb{R})$)then we prove the existence of weak energy solution in finite time but thedensity remains a priori discontinuous on the time interval of existence.

Vortex solutions for the compressible Navier-Stokes equations with general viscosity coefficients in 1D: regularizing effects or not on the density