Mecânica dos fluidos como um sistema vinculado

Abstract

In this dissertation was showed a study in fluids dynamic, where it was discussed the basic equations of fluids, for example, the Navier-Stokes equations and the continuity equations in differentials form and in the tensorial form. It was also presented an analogy between Maxwell equations and fluids equations. This analogy allows writing the equations of fluids in a linear form as the electromagnetism equations. Thus, using this analogy one can do a Lagrangian and a Hamiltonian formulation for fluids. Treating this system as constrained system and applying quantum field theory methods in the study of fluids dynamic. We first use a symplectic method to obtain the commutators for a compressible fluid. In this case, the commutators were obtained using the Lorentz gauge to broken the gauge symmetry.