PERIODIC PERTURBATIONS OF A COMPOSITE WAVE OF TWO VISCOUS SHOCKS FOR 1-D FULL COMPRESSIBLE NAVIER-STOKES EQUATIONS

This paper is concerned with the asymptotic stability of a composite wave of two viscous shocks under spatially periodic perturbations for the 1-d full compressible Navier--Stokes equations. It is proved that as time increases, the solution approaches the background composite wave with a shift for each shock, where the shifts can be uniquely determined if both the periodic perturbations and strengths of two shocks are small. The key of the proof is to construct a suitable ansatz such that the antiderivative method works.