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Author:

Liu, Lingjun (Liu, Lingjun.) | Wang, Danli (Wang, Danli.) | Xu, Lingda (Xu, Lingda.)

Indexed by:

Scopus SCIE

Abstract:

Considering the space-periodic perturbations, we prove the time-asymptotic stability of the composite wave of a viscous contact wave and two rarefaction waves for the Cauchy problem of 1-D compressible Navier-Stokes equations in this paper. Perturbations of this kind oscillate in the far field and are not integrable. The key is to construct a suitable ansatz carrying the same oscillation as that of the initial data, but due to the degeneration of contact discontinuity, the construction is more subtle. A novel method for constructing robust ansatzes is presented. It allows the same weight function to be used on different variables and wave patterns while maintaining control over the errors. As a result, it is possible to apply this construction to contact discontinuities and composite waves. Lastly, we demonstrate that the Cauchy problem admits a unique global-in-time solution and the composite wave remains stable under space-periodic perturbations through the energy method. (c) 2022 Elsevier Inc. All rights reserved.

Keyword:

Periodic perturbation Composite wave Navier-Stokes equations

Author Community:

  • [ 1 ] [Liu, Lingjun]Beijing Univ Technol, Fac Sci, Dept Math, Beijing 100124, Peoples R China
  • [ 2 ] [Wang, Danli]Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China
  • [ 3 ] [Wang, Danli]Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
  • [ 4 ] [Xu, Lingda]Tsinghua Univ, Yau Math Sci Ctr, Dept Math, Beijing 100084, Peoples R China
  • [ 5 ] [Xu, Lingda]Yanqi Lake Beijing Inst Math Sci & Applicat, Beijing 101408, Peoples R China

Reprint Author's Address:

  • [Wang, Danli]Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China;;

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Source :

JOURNAL OF DIFFERENTIAL EQUATIONS

ISSN: 0022-0396

Year: 2023

Volume: 346

Page: 254-276

2 . 4 0 0

JCR@2022

ESI Discipline: MATHEMATICS;

ESI HC Threshold:9

Cited Count:

WoS CC Cited Count: 4

SCOPUS Cited Count: 4

ESI Highly Cited Papers on the List: 0 Unfold All

WanFang Cited Count:

Chinese Cited Count:

30 Days PV: 9

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