An exact solution in a gravitating fluid with a density-dependent viscosity

An exact nonlinear solution for a cold fluid in presence of a gravitational field and viscous dissipation is obtained using Lagrange variable. It is shown that with a density-dependent viscosity the nonlinear equation can be exactly solved. The solution indicates that in absence of viscosity and initial fluid velocity shear, density collapse occurs at time of the order of inverse Jeans frequency. The effect of viscosity is to delay the collapse but it can not halt the collapse. The initial fluid velocity shear can act in both directions: a positive one leads to delay, a negative one to a speeding up of the density collapse. This nonlinear solution may have some bearing with the structure formations in the universe.