Resumen de Geometrodynamics of some non-relativistic incompressible fuids.

Agostino Pràstaro

• In some previous papers [1, 2] we proposed a geometric formulation of continuum mechanics, where a continuous body is seen as a suitable differentiable fiber bundle C on the Galilean space-time M, beside a differential equation of order k, Ek(C), on C and the assignement of a frame Psi on M. This approach allowed us to treat continuum mechanics as a unitary field theory and to consider constitutive and dynamical properties in a more natural way. Further, the particular intrinsic geometrical framework allowed to utilize directly the formal theory of differential equations in order to obtain criteria of existence of solutions.

  In the present paper we apply this general theory to some incompressible fluids. The scope is to demostrate that also for these more simple materials our theory is a suitable tool in order to understand better the fundamental principles of continuum mechanics.