• xmlui.mirage2.page-structure.header.title
    • français
    • English
  • Help
  • Login
  • Language 
    • Français
    • English
View Item 
  •   BIRD Home
  • CEREMADE (UMR CNRS 7534)
  • CEREMADE : Publications
  • View Item
  •   BIRD Home
  • CEREMADE (UMR CNRS 7534)
  • CEREMADE : Publications
  • View Item
JavaScript is disabled for your browser. Some features of this site may not work without it.

Browse

BIRDResearch centres & CollectionsBy Issue DateAuthorsTitlesTypeThis CollectionBy Issue DateAuthorsTitlesType

My Account

LoginRegister

Statistics

Most Popular ItemsStatistics by CountryMost Popular Authors
Thumbnail - No thumbnail

Existence and stability of steady compressible Navier–Stokes solutions on a finite interval with noncharacteristic boundary conditions

Melinand, Benjamin; Zumbrun, Kevin (2019), Existence and stability of steady compressible Navier–Stokes solutions on a finite interval with noncharacteristic boundary conditions, Physica D: Nonlinear Phenomena, 394, 1, p. 16-25. 10.1016/j.physd.2019.01.006

Type
Article accepté pour publication ou publié
External document link
https://hal.archives-ouvertes.fr/hal-01625910v1
Date
2019
Journal name
Physica D: Nonlinear Phenomena
Volume
394
Number
1
Publisher
Elsevier
Pages
16-25
Publication identifier
10.1016/j.physd.2019.01.006
Metadata
Show full item record
Author(s)
Melinand, Benjamin
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Zumbrun, Kevin
Department of mathematics [Bloomington]
Abstract (EN)
We study existence and stability of steady solutions of the isentropic compressible Navier–Stokes equations on a finite interval with noncharacteristic boundary conditions, for general not necessarily small-amplitude data. We show that there exists a unique solution, about which the linearized spatial operator possesses (i) a spectral gap between neutral and growing/decaying modes, and (ii) an even number of nonstable eigenvalues (with a nonnegative real part). In the case that there are no nonstable eigenvalues, i.e., of spectral stability, we show this solution to be nonlinearly exponentially stable in . Using “Goodman-type” weighted energy estimates, we establish spectral stability for small-amplitude data. For large-amplitude data, we obtain high-frequency stability, reducing stability investigations to a bounded frequency regime. On this remaining, bounded-frequency regime, we carry out a numerical Evans function study, with results again indicating universal stability of solutions.
Subjects / Keywords
Stability of steady waves; Bounded domains; Isentropic gas; Evans function

Related items

Showing items related by title and author.

  • Thumbnail
    New effective pressure and existence of global strong solution for compressible Navier-Stokes equations with general viscosity coefficient in one dimension 
    Burtea, Cosmin; Haspot, Boris (2020) Article accepté pour publication ou publié
  • Thumbnail
    Porous media equations, fast diffusion equations and the existence of global weak solution for the quasi-solution of compressible Navier-Stokes equations 
    Haspot, Boris (2014) Communication / Conférence
  • Thumbnail
    From the Highly Compressible Navier–Stokes Equations to Fast Diffusion and Porous Media Equations. Existence of Global Weak Solution for the Quasi-Solutions 
    Haspot, Boris (2016) Article accepté pour publication ou publié
  • Thumbnail
    Existence of global strong solution for the compressible Navier-Stokes equations with degenerate viscosity coefficients in 1D 
    Haspot, Boris (2018) Article accepté pour publication ou publié
  • Thumbnail
    Existence of global strong solution for the compressible Navier-Stokes system and the Korteweg system in two-dimension 
    Haspot, Boris (2013) Article accepté pour publication ou publié
Dauphine PSL Bibliothèque logo
Place du Maréchal de Lattre de Tassigny 75775 Paris Cedex 16
Phone: 01 44 05 40 94
Contact
Dauphine PSL logoEQUIS logoCreative Commons logo