This Project Grant from the National Science Foundation's Division of Mathematical Sciences, under the Mathematical and Physical Sciences program (CFDA 47.049), provides $253,285 to the University of Pittsburgh to support research seeking to advance the mathematical theory of free-surface water waves and compressible fluids governed by the Euler equations. Over a three-year period from September 1, 2022 through August 31, 2025, the University of Pittsburgh will conduct research to develop new or extend existing analytic techniques establishing existence and stability theory for steady water waves. It will also investigate uniqueness properties for weak solutions to one-dimensional systems of compressible gases. The research aims to enhance understanding of ideal fluid mathematics and develop novel tools for truly nonlinear phenomena in partial differential equations. Graduate students and postdoctoral researchers will collaborate on the research, which brings new perspectives to fundamental problems in ideal fluids, including constructing large-amplitude solitary water waves and studying stability of solitary waves and non-uniqueness of entropy solutions.
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