Analysis of Mathematical models for the ocean, atmospherics sciences and optics.

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This project concerns the analysis of Partial Differential Equations arising from quantum mechanics, geometric optics and fluid mechanic. More specifically, it focuses on the one hand on, the Nonlinear Schrödinger and Nonlinear Wave equations (as models for dispersive equations), and on the other hand on, the Navier-Stokes, Boussinesq, the primitive equations and related fluid models.**Although the modeling, physical and the computational parts were very well developed for fluid models, the mathematical study did not seem to follow the same stream of progress. Meanwhile and during the last two decades, a tremendous progress has been made in the analysis of dispersive partial differential equations. So that comes the natural question on how one can use and take advantage of those new techniques and tools to further analyze the partial differential equations coming from fluid dynamic. One can already observe the beginning of this in several recent attempts. So the general purpose of this project is to bring together ideas and techniques from these seemingly different kinds of Analysis of PDEs in order to make progress on the mathematical understanding of turbulence and many other relevant physical phenomena.