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Existence and Uniqueness of Strong Stationary Solutions for Compressible Flows

In: Handbook of Mathematical Analysis in Mechanics of Viscous Fluids

Author

Listed:
  • Ondřej Kreml

    (Czech Academy of Sciences, Institute of Mathematics)

  • Piotr Bogusł aw Mucha

    (University of Warsaw, Institute of Applied Mathematics and Mechanics)

  • Milan Pokorný

    (Charles University, Faculty of Mathematics and Physics)

Abstract

This chapter contains a survey of results in the existence theory of strong solutions to the steady compressible Navier-Stokes system. In the first part, the compressible Navier-Stokes equations are studied in bounded domains, both for homogeneous (no inflow) and inhomogeneous (inflow) boundary conditions. The solutions are constructed in Sobolev spaces. The next part contains the results for unbounded domains, especially for the exterior domains. Here, not only the question of existence and uniqueness is considered, but also the asymptotic structure near infinity is studied. Due to the different nature of the problems, the two- and three-dimensional problems are treated separately.

Suggested Citation

  • Ondřej Kreml & Piotr Bogusł aw Mucha & Milan Pokorný, 2018. "Existence and Uniqueness of Strong Stationary Solutions for Compressible Flows," Springer Books, in: Yoshikazu Giga & Antonín Novotný (ed.), Handbook of Mathematical Analysis in Mechanics of Viscous Fluids, chapter 47, pages 2663-2719, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-13344-7_65
    DOI: 10.1007/978-3-319-13344-7_65
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