Existence, stability and long time behaviour of weak solutions of the three-dimensional compressible Navier-Stokes equations with potential force

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Abstract

We address the global-in-time existence, stability and long time behaviour of weak solutions of the three-dimensional compressible Navier-Stokes equations with potential force. We show the details of the α-dependence of different smoothing rates for weak solutions near t = 0 under the assumption on the initial velocity u0 that u0∈Hα for α ∈ (½,1] and obtain long time convergence of weak solutions in various norms. We then make use of the Lagrangian framework in comparing the instantaneous states of corresponding fluid particles in two different solutions. The present work provides qualitative results on the long time behaviour of weak solutions and how the weak solutions depend continuously on initial data and steady states. Copyright © 2021 Elsevier Inc. All rights reserved.
Original languageEnglish
Pages (from-to)463-512
JournalJournal of Differential Equations
Volume299
Early online dateAug 2021
DOIs
Publication statusPublished - Oct 2021

Citation

Suen, A. (2021). Existence, stability and long time behaviour of weak solutions of the three-dimensional compressible Navier-Stokes equations with potential force. Journal of Differential Equations, 299, 463-512. doi: 10.1016/j.jde.2021.07.027

Keywords

  • Navier-Stokes equations
  • Compressible flow
  • Potential force
  • Stability
  • Long time behaviour

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