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Weak Solutions, A Priori Estimates

  • Eduard Feireisl
  • Antonín Novotný
Chapter
Part of the Advances in Mathematical Fluid Mechanics book series (AMFM)

Abstract

The fundamental laws of continuum mechanics that can be interpreted as infinite families of integral identities equivalent to systems of partial differential equations give rise to the concept of weak (or variational) solutions that can be vastly extended to extremely divers physical systems of various sorts. We introduce the concept of weak solution to the Navier-Stokes-Fourier system based postulating, besides the principles of mass and momentum conservation, a variational form of the total energy balance and the entropy balance inequality. Basic a priori bounds are derived.

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Eduard Feireisl
    • 1
  • Antonín Novotný
    • 2
  1. 1.ASCR Praha Mathematical InstitutePraha 1Czech Republic
  2. 2.Université de Toulon, IMATHLa GardeFrance

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