The goal of this project is to pursue new methods in the mathematical analysis of non-local and non-linear
partial differential equations. For this purpose we present several physical scenarios of interest in the context
of incomp...
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Descripción del proyecto
The goal of this project is to pursue new methods in the mathematical analysis of non-local and non-linear
partial differential equations. For this purpose we present several physical scenarios of interest in the context
of incompressible fluids, from a mathematical point of view as well as for its applications: both from the
standpoint of global well-posedness, existence and uniqueness of weak solutions and as candidates for blowup.
The equations we consider are the incompressible Euler equations, incompressible porous media equation
and the generalized Quasi-geostrophic equation. This research will lead to a deeper understanding of the nature
of the set of initial data that develops finite time singularities as well as those solutions that exist for all time for incompressible flows.