Variational Formulations for Viscous Flow

For physical systems, the dynamics of which is formulated within the framework of Lagrange formalism the dynamics is completely defined by only one function, namely the Lagrangian. As well‐known the whole conservative Newtonian mechanics has been successfully embedded into this methodical concept. Different from this, in continuum theories many open questions remain up to date, especially when considering dissipative processes. The viscous flow of a fluid, given by the Navier‐Stokes equations is a typical example for this. In this contribution a special approach for finding a Lagrangian for viscous flow is suggested and discussed. The equations of motion resulting from the respective Lagrangian are compared to the Navier‐Stokes equations and differences are discussed. For a simple flow example their solution is compared to the one resulting from Navier‐Stokes equations. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)