In search of a variational formulation of the relativistic Navier‐Stokes equations

Abstract

AbstractDrawing an analogy with Maxwell theory a new Lagrangian is proposed for a variational formulation of the relativistic Navier‐Stokes equations which to‐date has remained elusive. A key feature is the use of tensor potentials, whose degrees of gauge freedom allow for the reformulation of the energy‐momentum equations in a self‐adjoint form. An already existing potential‐based representation of the relativistic field equations is a suitable starting point for the present considerations, which in turn are guided by the already successfully solved case of non‐relativistic, stationary and incompressible flow.