Nonlinear Evolution Equations

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In this project, the principal investigator and his collaborators propose to develop new methods and techniques that will provide a better understanding of the qualitative behavior of solutions of dispersive models. These models describe relevant physical phenomena, including several arising in fluid mechanics and in wave propagation. In a multidisciplinary approach, these innovative methods will improve the design of efficient numerical tools in the study of some outstanding problems in fluids dynamics. Also, they will establish new parameters in the modeling and simulation for these types of systems.To achieve the aforementioned goals, the principal investigator and the project's other participants will continue the development of powerful analytic techniques mainly coming from harmonic analysis. While the new approaches will be focused in concrete nonlinear problems, their applicability will be broad. This is of potential interest to researchers in other disciplines. The principal investigator will disseminate his results as widely as possible through expositions at professional meetings and electronic publications. Research and education will be vigorously integrated with special efforts to promote and broaden the participation of underrepresented groups, with the active participation of undergraduates, with innovative pedagogical initiatives and modes of collaboration.