Some viscous flows that implement the principle of minimum dissipation of kinetic energy. (English. Russian original) Zbl 1014.76017

Comput. Math. Math. Phys. 39, No. 12, 2015-2019 (1999); translation from Zh. Vychisl. Mat. Mat. Fiz. 39, No. 12, 2098-2103 (1999).
Summary: The Helmholtz-Korteweg principle is a widely known principle of viscous incompressible fluid dynamics. The stationary point of the kinetic-energy-dissipation functional corresponds to linear Stokes equations describing slow creeping motions of viscous incompressible fluids. The behavior of the kinetic-energy-dissipation functional is analyzed here for internal flows of viscous fluids described by equations of motion different from Stokes equations.


76D99 Incompressible viscous fluids
76M30 Variational methods applied to problems in fluid mechanics