### Abstract

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 language | English |
---|---|

Pages (from-to) | 921-935 |

Number of pages | 15 |

Journal | Progress of Theoretical Physics |

Volume | 127 |

Issue number | 5 |

DOIs | |

Publication status | Published - 2012 May |

### Fingerprint

### ASJC Scopus subject areas

- Physics and Astronomy (miscellaneous)

### Cite this

*Progress of Theoretical Physics*,

*127*(5), 921-935. https://doi.org/10.1143/PTP.127.921

**A variational principle for dissipative fluid dynamics.** / Fukagawa, Hiroki; Fujitani, Youhei.

Research output: Contribution to journal › Article

*Progress of Theoretical Physics*, vol. 127, no. 5, pp. 921-935. https://doi.org/10.1143/PTP.127.921

}

TY - JOUR

T1 - A variational principle for dissipative fluid dynamics

AU - Fukagawa, Hiroki

AU - Fujitani, Youhei

PY - 2012/5

Y1 - 2012/5

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84862532800&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84862532800&partnerID=8YFLogxK

U2 - 10.1143/PTP.127.921

DO - 10.1143/PTP.127.921

M3 - Article

AN - SCOPUS:84862532800

VL - 127

SP - 921

EP - 935

JO - Progress of Theoretical Physics

JF - Progress of Theoretical Physics

SN - 0033-068X

IS - 5

ER -