2 Mathematical theory of fluid dynamics 2 2.1 Thermal systems in equilibrium . . . . . . . . . . . . . . . . . . . 3 2.2 Gibbs’ equation and thermodynamic stability . . . . . . . . . . . 3 2.3 Balance laws . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.4 Description of motion, velocity . . . . . . . . . . . . . . . . . . . 6 2.5 Energy, entropy, Second law of thermodynamics . . ....

A new mixed variational formulation of the equations of stationary incompressible magneto–hydrodynamics is introduced and analyzed. The formulation is based on curl-conforming Sobolev spaces for the magnetic variables and is shown to be well-posed in (possibly non-convex) Lipschitz polyhedra. A finite element approximation is proposed where the hydrodynamic unknowns are discretized by standard ...

We derive boundary conditions for the vorticity equation with solid wall boundaries. The formulation uses a Dirichlet condition for the normal component of vorticity, and Neumann type conditions for the tangential components. In a Galerkin (integral) formulation the tangential condition is natural, i.e. it is enforced by a right-hand side functional and does not impose a boundary constraint on ...

In this paper, we consider an extended formulation of the transport equation that remains meaningful with discontinuous velocity fields b, assuming that (1, b) is a special function of bounded deformation (SBD). We study existence, uniqueness, and continuity/stability of the presented formulation. We then apply this study to the problem of fitting to available data a space-time image subject to...

We derive boundary conditions for the vorticity equation with solid wall boundaries. The formulation uses a Dirichlet condition for the normal component of vorticity, and Neumann type conditions for the tangential components. In a Galerkin (integral) formulation the tangential condition is natural, i.e. it is enforced by a right-hand side functional and does not impose a boundary constraint on ...