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Incompressible fluid dynamics equations


In this research project we propose the study of solutions of equations arising from the fluiddynamics from an analytical point-of-view, especially the Euler and Navier-Stokes equations. Some fundamental questions such as global existence and uniqueness of solution in some caseshave not yet been fully understood and the aim of this project is to enhance the understanding of such issues. In order to do so, we propose the study of the following topics: existence of energy dissipative incompressible flows; analysis of blow-up scenarios for the Euler equations and for related equations; analysis of incompressible ideal flows with symmetry. In addition, in pursuence of obtaining a rigorous mathematical formalization of the conventional theory of turbulence we propose the development of a complete abstract theory of statistics solutions for evolution equations. (AU)

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