We establish the time-asymptotic stability of generic Riemann solutions to the one-dimensional compressible Navier–Stokes–Fourier equations. The Riemann solution under consideration is a generic combination of a shock, a contact discontinuity, and a rarefaction wave. We prove that the perturbed solution of Navier–Stokes–Fourier converges, uniformly in space as time goes to infinity, to an ansatz composed of viscous shock with time-dependent shift, a viscous contact wave and an inviscid rarefaction wave. This is a first resolution of the time-asymptotic stability of three waves of different kinds associated with the generic Riemann solutions. Our approach relies on the method of a-contraction with shifts and relative entropy, specifically applied to both the shock wave and the contact wave. It enables the application of a global energy method for the generic combination of three waves.
Publication: Arch. Rational Mech. Anal. (2025)
https://doi.org/10.1007/s00205-025-02116-w
Author: M.-J. Kang,Department of Mathematical Sciences, Korea Advanced Institute of Science and Technology, Daejeon 34141 Korea.
e-mail: moonjinkang@kaist.ac.kr
A. F. Vasseur, Department of Mathematics, The University of Texas at Austin, Austin TX 78712 USA.
e-mail: vasseur@math.utexas.edu
Y. Wang，State Key Laboratory of Mathematical Sciences and Institute of Applied Mathematics, AMSS, Chinese Academy of Sciences, Beijing 100190 People’s Republic of China.
e-mail: wangyi@amss.ac.cn
Y. Wang，School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing，100049 People’s Republic of China.
附件下载：
