A variational principle for dissipative fluid dynamics

Hiroki Fukagawa, Youhei Fujitani

Research output: Contribution to journalArticlepeer-review

19 Citations (Scopus)


In the variational principle leading to the Euler equation for a perfect fluid, we can use the method of undetermined multiplier for holonomic constraints representing mass conservation and adiabatic condition. For a dissipative fluid, the latter condition is replaced by the constraint specifying how to dissipate. Noting that this constraint is nonholonomic, we can derive the balance equation of momentum for viscous and viscoelastic fluids by using a single variational principle. We can also derive the associated Hamiltonian formulation by regarding the velocity field as the input in the framework of control theory.

Original languageEnglish
Pages (from-to)921-935
Number of pages15
JournalProgress of Theoretical Physics
Issue number5
Publication statusPublished - 2012 May

ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)


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