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Dynamical Stability of Non-Constant Equilibria for the Compressible Navier-Stokes Equations in Eulerian Coordinates

Dynamical Stability of Non-Constant Equilibria for the Compressible Navier-Stokes Equations in Eulerian Coordinates

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KOTSCHOTE, Matthias, 2014. Dynamical Stability of Non-Constant Equilibria for the Compressible Navier-Stokes Equations in Eulerian Coordinates. In: Communications in Mathematical Physics. 328(2), pp. 809-847. ISSN 0010-3616. eISSN 1432-0916. Available under: doi: 10.1007/s00220-014-2023-z

@article{Kotschote2014Dynam-29975, title={Dynamical Stability of Non-Constant Equilibria for the Compressible Navier-Stokes Equations in Eulerian Coordinates}, year={2014}, doi={10.1007/s00220-014-2023-z}, number={2}, volume={328}, issn={0010-3616}, journal={Communications in Mathematical Physics}, pages={809--847}, author={Kotschote, Matthias} }

eng In this paper we establish global existence and uniqueness of strong solutions to the non-isothermal compressible Navier–Stokes equations in bounded domains. The initial data have to be near equilibria that may be non-constant due to considering large external forces. We are able to show exponential stability of equilibria in the phase space and, above all, to study the problem in Eulerian coordinates. The latter seems to be a novelty, since in works by other authors, global strong L <sub>p</sub> -solutions have been investigated only in Lagrangian coordinates; Eulerian coordinates are even declared as impossible to deal with. The proof is based on a careful derivation and study of the associated linear problem. 2015-02-23T14:58:10Z 2015-02-23T14:58:10Z Kotschote, Matthias Dynamical Stability of Non-Constant Equilibria for the Compressible Navier-Stokes Equations in Eulerian Coordinates 2014 Kotschote, Matthias

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