Operador de Poisson para la descripción de un fluido euleriano en tres dimensiones

Abstract

In this work we study the motion of an incompressible inviscid fluid on a three-dimensional domain. Taking into account that the Hamiltonian systems allow us to study the time-evolution systems, we analyze a Hamiltonian formulation for this fluid. With this aim in mind, we begin with the basis of this theory to extend some concepts. When we analyze the motion of this fluid, we notice that we are working with an infinite-dimensional system. We work with Eulerian variables to obtain the Euler equations. We study the spaces where these equations are formulated and we obtain a space where two of these equations are satisfied. Later we work with the residual equation and formulate it as a Hamiltonian system regarding the velocity. When we work with a domain of R2, there exist also a Hamiltonian formulation regarding the vortex for this equation. In the case of R3, we want to know how possible is to extend that. We study subspaces where is possible to analyze the Euler equation regarding the vortex, and we study about the new problems encountered.