# Existence of global strong solution for compressible Navier Stokes equations in one dimension with for degenerate viscosity coefficients

In this talk we prove the existence of global strong solution for the Navier-Stokes equations with general degenerate viscosity coefficients in one dimension. The cornerstone of the proof is the introduction of a new effective pressure which allows to obtain an Oleinik-type estimate for the so called effective velocity. It enables us to control the $L^\infty$ norm of $\frac{1}{\rho}$ with $\rho$ the density. In our proof we make use also of additional regularizing effects on the velocity which requires to extend the techniques developed by Hoff for the constant viscosity case.

This talk is part of the Geometric Analysis and Partial Differential Equations seminar series.