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Existence of Stationary Weak Solutions for Isentropic and Isothermal Compressible Flows

In: Handbook of Mathematical Analysis in Mechanics of Viscous Fluids

Author

Listed:
  • Song Jiang

    (Institute of Applied Physics and Computational Mathematics)

  • Chunhui Zhou

    (Southeast University, Department of Mathematics)

Abstract

The aim of this chapter is to study the existence of weak solutions to the multidimensional steady isentropic and isothermal compressible Navier-Stokes equations with large external forces. In the past decades, significant progress has been made on the existence of large weak solutions. In this chapter, a brief review of recent existence results on the existence of (renormalized) stationary weak solutions with large external forces will be presented. Different boundary value problems, such as the spatially periodic, slip and Dirichlet boundary value problems, will be investigated, and some related topics such as nonuniqueness, regularity, etc., will also be discussed. The ideas and developed techniques used in analysis will be presented and analyzed, and some open problems will be addressed.

Suggested Citation

  • Song Jiang & Chunhui Zhou, 2018. "Existence of Stationary Weak Solutions for Isentropic and Isothermal Compressible Flows," Springer Books, in: Yoshikazu Giga & Antonín Novotný (ed.), Handbook of Mathematical Analysis in Mechanics of Viscous Fluids, chapter 45, pages 2549-2594, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-13344-7_63
    DOI: 10.1007/978-3-319-13344-7_63
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