EXISTENCE OF UNBOUNDED SOLUTIONS TO A ONE DIMENSIONAL ISENTROPIC PERIODIC FLOW OF A COMPRESSIBLE VISCOUS FLUID WITH SELF-GRAVITATION

Abstract

We consider a one dimensional isentropic periodic flow of a compressible viscous fluid driven by a self-gravitation of the fluid. We show the existence of an unbounded solution of a system describing the flow. A sufficient condition for the unboundedness is given in terms of the initial values of an energy form.