Project Grant 2307680

The University of California, Davis was awarded a $242,333 project grant from the National Science Foundation Division of Mathematical Sciences under the Mathematical and Physical Sciences federal grant program (CFDA 47.049). The grant supports research to develop new analytical and geometric frameworks to describe the formation and propagation of shock waves in fluid dynamics. Specifically, the university will conduct collaborative research to better understand shock formation, shock development, and the propagation of singularities in compressible fluids like gases and plasmas. This includes studying how smooth initial data evolves over time and results in cusp-like singularities where fluid properties become infinite. The grant also enables investigation into how shock surfaces and weak characteristic discontinuities emerge from pre-shock conditions. Finally, the research will explore extending the developed frameworks to more complex physical models like magnetohydrodynamic equations describing plasma flows. The award period is from July 1, 2023 through June 30, 2028.