Qualitative studies of the Navier-Stokes and related systems

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The project addresses qualitative properties of solutions of the Navier-Stokes and related equations arising in fluid dynamics, including the Euler and Primitive equations. We will investigate the properties of small scales in a turbulent flow by estimating the complexity of solutions and study the relationship with the problems regarding observables and degrees of freedom in a fluid. A considerable effort will be dedicated to a fluid-structure models (local and global existence, regularity) and other complex PDE systems involving a fluid boundary. We will also study the properties solutions of the viscous and inviscid primitive equation of the ocean and the atmosphere. We will especially be interested in local and global existence of solutions and their asymptotic behavior.The mathematical study of fluids is of fundamental importance in meteorology, science, and engineering. The project seeks better understanding of the fluid motion especially on small scales which are of interest in turbulence. The special emphasis is going to be placed on the primitive equations which constitute the basic model for weather prediction and on the fluid-structure systems modeling interaction of a fluid with an elastic body.