Stabilizing effect of the power law inflation on isentropic relativistic fluids

This paper is concerned with the stabilizing effect of the power law inflation on relativistic Eulerian fluids. We prove the global stability of the background solutions to the relativistic fluids including the isothermal gases and generalized Chaplygin gases by the method of conformal transformation when the initial data is a small perturbation to the background solution. We also prove the blowup phenomena of the relativistic Euler fluids including the isothermal gases and polytropic gases when the initial data satisfies suitable assumptions.