This $124,914 project grant from the National Science Foundation Division of Mathematical Sciences, under the Mathematical and Physical Sciences program (CFDA 47.049), will fund collaborative research between U.S. and U.K. mathematicians to develop innovative methods for studying stability questions in nonlinear partial differential equations across scales. The University of Texas at Austin will partner with other institutions to conduct research, workshops, and student involvement from August 1, 2022 to July 31, 2025.
Key objectives include stability analysis of shock wave patterns, vortex sheets, contact discontinuities, and other characteristic discontinuities. Additionally, the team aims to analyze particle to continuum limits, including asymptotic, mean-field and large-time behavior in pairwise and general particle interactions, as well as stability of asymptotic limits with emphasis on vanishing viscosity problems in compressible viscous flows. The research seeks new understanding of fundamental scientific issues while advancing nonlinear stability theory across multiscale applications.
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