Relaxed equations for nonhomogeneous, ideal hydrodynamics

Author(s)

Juliana Conceição Precioso

• Document type: Doctoral Thesis
• Press: Campinas, SP.
• Institution: Universidade Estadual de Campinas (UNICAMP). Instituto de Matemática, Estatística e Computação Científica
• Defense date: 2005-11-24

Examining board members

Helena Judith Nussenzveig Lopes; Benar Fux Svaiter; Clodoaldo Grotta Ragazzo; Djairo Guedes de Figueiredo; Renato Hyuda de Luna Pedrosa

• Advisor: Helena Judith Nussenzveig Lopes; Milton da Costa Lopes Filho

Abstract

In this work we deduce a new system of partial differential equations to describe incompressible flows of nonhomogeneous ideal fluids. We call this system "relaxed Euler equations". We show existence of weak solutions for the new model and consistency with the classical model given by the nonhomogeneous incompressible Euler equations. We show that a smooth solution of the Euler equations gives rise to a solution of the relaxed equations. Moreover, if the time T is sufficiently small, then this solution is the unique minimum for the associated action. Here, "sufficiently small" means to satisfy what is known as the Arnold criterion. We show also that, if a solution of the relaxed equations has an appropriate structure then it gives rise to a weak solution of the Euler equations (AU)