This $125,000 three-year Project Grant from the National Science Foundation Division of Mathematical Sciences, under the Mathematical and Physical Sciences program (CFDA 47.049), will support 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 research focuses on four objectives: stability analysis of shock wave patterns including gas dynamics problems; stability analysis of vortex sheets and discontinuities; stability analysis of particle-to-continuum limits, including mean-field limits for pairwise interactions and particle limits for general multi-agent systems; and stability analysis of asymptotic limits such as the vanishing viscosity limit of multidimensional compressible viscous to inviscid flows. The Pennsylvania State University will lead this collaborative effort to advance understanding of fundamental scientific issues in these areas and foster cross-fertilization, with the goal of making progress toward a nonlinear stability theory of nonlinear partial differential equations across multiscale applications.
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