It is well known that the rarefaction wave is one of the basic wave patterns of the hyperbolic conservation laws.  In this talk we prove time-asymptotic stability towards the rarefaction wave to the Quantum-Navier-Stokes equations in the one-dimensional space, provided that the strength of the wave is weak and the initial perturbation is small. The proof is mainly based on \( L^2 \)-energy method and some time-decay estimates in \( L^p \)-norm for the smoothed rarefaction wave.

stability，Navier-Stokes equations