Abstract：In this talk, I shall show the asymptotic stability of the rarefaction wave for the onedimensional compressible Euler system with nonlocal velocity alignment. For the initial data approaching to rarefaction wave, we prove the corresponding solution converges toward the rarefaction wave. We develop some promoted estimates for the smooth approximate rarefaction wave and new a priori estimates by Fourier analysis tools. Moreover, we introduce the weighted energy method and Besov spaces to obtain the key high-order derivative estimates, in which we overcome the difficulties by the nonlocal volecity alignment. It is worth mentioning that this is the first stability result of rarefaction wave for compressible Euler system with velocity alignment. This work jointed with Linan Li and Xiang Bai.
