This $105,999 National Science Foundation Mathematical and Physical Sciences project grant funds collaborative research between U.S. and U.K. mathematicians to develop innovative methods for analyzing the stability of nonlinear partial differential equations across scales. The University of Wisconsin-Madison leads the research team in studying challenging problems in fluid dynamics, including shock wave interactions, vortex sheet stability, and vanishing viscosity limits. The project also investigates particle systems as the number becomes infinite, with applications to physical, biological, financial and social systems involving interacting agents. The research focuses on stability analysis of shock patterns, vortex sheets and other discontinuities, as well as particle-to-continuum limits and asymptotic limits. The award period is from August 1, 2022 through July 31, 2025.
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