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.
CitationSuen, 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
- Navier-Stokes equations
- Compressible flow
- Potential force
- Long time behaviour