A free energy Lagrangian variational formulation of the Navier-Stokes-Fourier system

François Gay-Balmaz, Hiroaki Yoshimura

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2 Citations (Scopus)


We present a variational formulation for the Navier-Stokes-Fourier system based on a free energy Lagrangian. This formulation is a systematic infinite-dimensional extension of the variational approach to the thermodynamics of discrete systems using the free energy, which complements the Lagrangian variational formulation using the internal energy developed in [F. Gay-Balmaz and H. Yoshimura, A Lagrangian variational formulation for nonequilibrium thermodynamics, Part II: Continuum systems, J. Geom. Phys. 111 (2017) 194-212] as one employs temperature, rather than entropy, as an independent variable. The variational derivation is first expressed in the material (or Lagrangian) representation, from which the spatial (or Eulerian) representation is deduced. The variational framework is intrinsically written in a differential-geometric form that allows the treatment of the Navier-Stokes-Fourier system on Riemannian manifolds.

Original languageEnglish
Article number1940006
JournalInternational Journal of Geometric Methods in Modern Physics
Publication statusPublished - 2019 Feb 1


  • Navier-Stokes-Fourier system
  • Variational formulation
  • nonequilibrium thermodynamics

ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)


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