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Weak Solutions to 2D and 3D Compressible Navier-Stokes Equations in Critical Cases

In: Handbook of Mathematical Analysis in Mechanics of Viscous Fluids

Author

Listed:
  • P. I. Plotnikov

    (Novosibirsk State University, Mathematical Department
    Lavryentyev Institute of Hydrodynamics, Siberian Division of Russian Academy of Sciences)

  • W. Weigant

    (Universität Bonn, Institute für Angewandte Mathematik)

Abstract

In this chapter the compressible Navier-Stokes equations with the critical adiabatic exponents are considered. The crucial point in this situation are new estimates of the Radon measure of solutions. These estimates are applied to the boundary value problem for the compressible Navier-Stokes equations with the critical adiabatic exponents. The existence of weak solutions to 2D isothermal problem is proved. The cancelation of concentrations for 3D nonstationary initial-boundary value problem with the critical adiabatic exponent 3/2 is established.

Suggested Citation

  • P. I. Plotnikov & W. Weigant, 2018. "Weak Solutions to 2D and 3D Compressible Navier-Stokes Equations in Critical Cases," Springer Books, in: Yoshikazu Giga & Antonín Novotný (ed.), Handbook of Mathematical Analysis in Mechanics of Viscous Fluids, chapter 31, pages 1601-1671, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-13344-7_75
    DOI: 10.1007/978-3-319-13344-7_75
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