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| Author(s): |
Flavia Zechineli Fernandes
Total Authors: 1
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| Document type: | Doctoral Thesis |
| Press: | Campinas, SP. |
| Institution: | Universidade Estadual de Campinas (UNICAMP). Instituto de Matemática, Estatística e Computação Científica |
| Defense date: | 2005-09-11 |
| Examining board members: |
Milton da Costa Lopes Filho;
Max Oliveira de Souza;
Antonio Luiz Pereira;
José Luiz Boldrini;
Jaime Angulo Pava
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| Advisor: | Milton da Costa Lopes Filho |
| Abstract | |
In this work we shall prove the existence of weak solutions of the incompressible Euler equations in two-dimensional domains with smoothly moving boundaries. The main objective is to rebuild the work developed by Cheng He and Ling Hsiao (2000) with appropriate conditions for material domains. To show the existence of a weak solution for the Euler equations in a noncylindrical space-time domain, we start from a prescribed movement of the domain and we determine the boundary conditions assuming that the fluid does not cross the boundary. With this, we formulate the problem that will be studied and we reduce that problem to those with tangencial velocity field at the boundary. Then, by using elementary methods of differential geometry, we transform the equations with homogeneous boundary conditions in one in a cylindrical domain. We construct a family of approximate solutions utilizing the solutions to the Navier-Stokes equations in a corresponding time dependent domain with the modified boundary conditions. With those approximate solutions we get estimates which together with a compactness argument enables us to choose a subsequence of the aproximate solutions converging in L2 to a weak solution to the original problem. (AU) | |