Weak Solutions for the Compressible Navier-Stokes Equations: Existence, Stability, and Longtime Behavior

Antonín Novotný () and Hana Petzeltová ()
Additional contact information
Antonín Novotný: IMATH, Université de Toulon
Hana Petzeltová: Mathematical Institute of the Academy of Sciences of the Czech Republic, Department EDE

Chapter 29 in Handbook of Mathematical Analysis in Mechanics of Viscous Fluids, 2018, pp 1381-1546 from Springer

Abstract: Abstract This double-sized chapter contains two related themes that were supposed to be covered by two independent chapters of the handbook in the original project: (1) weak solutions of the Navier-Stokes equations in the barotropic regime and (2) weak solutions of the Navier-Stokes-Fourier system. We shall discuss for both systems: (1) Various notions of weak solutions, their relevance, and their mutual relations. (2) Global existence of weak solutions. (3) Notions of relative energy functional, dissipative solutions and relative energy inequality and its impact on the investigation of the stability analysis of compressible flows. (4) Weak strong uniqueness principle. (5) Longtime behavior of weak solutions. For physical reasons, we shall limit ourselves to the three-dimensional physical space.

Date: 2018
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-13344-7_76

Ordering information: This item can be ordered from
http://www.springer.com/9783319133447

DOI: 10.1007/978-3-319-13344-7_76

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().