TY - JOUR
T1 - A free energy Lagrangian variational formulation of the Navier-Stokes-Fourier system
AU - Gay-Balmaz, François
AU - Yoshimura, Hiroaki
N1 - Funding Information:
F.G.B. is partially supported by the ANR project GEOMFLUID, ANR-14-CE23-0002-01; H.Y. is partially supported by JSPS Grant-in-Aid for Scientific Research (26400408, 16KT0024, 24224004) and the MEXT “Top Global University Project”.
Publisher Copyright:
© 2019 World Scientific Publishing Company.
PY - 2019/2/1
Y1 - 2019/2/1
N2 - 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.
AB - 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.
KW - Navier-Stokes-Fourier system
KW - Variational formulation
KW - nonequilibrium thermodynamics
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U2 - 10.1142/S0219887819400061
DO - 10.1142/S0219887819400061
M3 - Article
AN - SCOPUS:85058146443
SN - 0219-8878
VL - 16
JO - International Journal of Geometric Methods in Modern Physics
JF - International Journal of Geometric Methods in Modern Physics
M1 - 1940006
ER -