 Local and Global Existence of Strong Solutions for the Compressible Navier-Stokes Equations Near Equilibria via the Maximal RegularityMatthias Kotschote ()
Chapter 36 in Handbook of Mathematical Analysis in Mechanics of Viscous Fluids, 2018, pp 1905-1946 from Springer Abstract: Abstract The purpose of this contribution is to show how the maximal regularity method can serve to prove existence of strong solutions to the Navier-Stokes equations. In order to illustrate the method, existence and uniqueness of global solutions to the Navier-Stokes equations for compressible fluids with or without heat conductivity in bounded domains shall be proved. The initial data have to be near equilibria that may be nonconstant due to considering large external potential forces. The exponential stability of equilibria in the phase space is shown and, above all, the problem is studied in Eulerian coordinates. The latter seems to be a novelty, since in works by other authors, global strong L p -solutions have been investigated only in Lagrangian coordinates; Eulerian coordinates are even declared as impossible to deal with, cf. on page 418 in Mucha, Zaja̧czkowski (ZAMM 84(6):417–424, 2004). The proof is based on a careful derivation and study of the associated linear problem. Date: 2018 There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it. Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-13344-7_50 Ordering information: This item can be ordered from DOI: 10.1007/978-3-319-13344-7_50 Access Statistics for this chapter More chapters in Springer Books from Springer |
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