The key purpose of this work is to study an array of problems related to the flow of an ideal fluid. Though the subject of mathematical fluid dynamics is quite old, there is still a great number of open problems--indeed open fields--that have not been solved and/or considered. At the heart of the study of the Euler equations is the non-locality, which is brought forth by the presence of the pressure term. In this thesis we will discuss some important features of the Euler equations including: well/ill posedness in critical spaces vis a vis the spontaneous formation of small scales as well as a study of the vanishing viscosity limit in critical spaces. We will also discuss two other related models: one from the study of active scalar equations and the other from viscoelasticity. The final chapter is about the vanishing viscosity limit for the free-boundary Navier Stokes equations with surface tension.
|Advisor:||Masmoudi, Nader, Lin, Fang-Hua|
|Commitee:||Germain, Pierre, Kohn, Robert, Shatah, Jalal|
|School:||New York University|
|School Location:||United States -- New York|
|Source:||DAI-B 76/01(E), Dissertation Abstracts International|
|Keywords:||Euler equations, Incompressible flows, Navier Stokes equations, Vanishing viscosity|
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