Time-Asymptotic Stability of Composite Wave for the One-Dimensional Compressible Fluid of Korteweg Type
Abstract
Abstract. We study the asymptotic stability of a composition of rarefaction and shock waves for the one-dimensional barotropic compressible fluid of Korteweg-type, called the Navier–Stokes–Korteweg (NSK) system. Precisely, we show that the solution to the NSK system asymptotically converges to the composition of the rarefaction wave and shifted viscous-dispersive shock wave, under a certain smallness assumption on the initial perturbation and strength of the waves. Our method is based on the method of [Formula: see text]-contraction with shift developed by Kang and Vasseur [ Arch. Ration. Mech. Anal., 222 (2016), pp. 343–391], successfully applied to obtain contraction or stability of nonlinear waves for hyperbolic systems.
Fields of Study & Subjects
Navier-Stokes equation solutions
Ocean Waves and Remote Sensing
Thermoelastic and Magnetoelastic Phenomena
Publication details
- Journal / source
- SIAM Journal on Mathematical Analysis
- Publisher
- Society for Industrial & Applied Mathematics (SIAM)
- Volume
- 58
- Issue
- 1
- Pages
- 547–597
- Publication date
- 30 January 2026
- Language
- EN