This federal Project Grant award for $209,999.00, provided by the National Science Foundation's (NSF) Mathematical and Physical Sciences (CFDA 47.049) program, supports research on the theoretical understanding of partial differential equations arising from physics. The key research goals of the project include:
Establishing the well-posedness and conditional regularity theory for the relativistic Landau equations, with a focus on the dynamics of slower-than-light mass spreading.
Creating a rigorous mathematical study on the effect of evaporative cooling in a self-gravitating gas cluster with particle collisions, where gravity and thermodynamics pull the solution towards different equilibria.
Exploring boundary interactions in kinetic equations and whether these can be recovered as a limit of boundaryless "force field" interactions.
Investigating the behavior of kinetic equations near known self-similar shock profiles for compressible fluid equations.
The award, with a project period from August 1, 2024 to July 31, 2027, is funded to Louisiana State University and Agricultural and Mechanical College to advance the theoretical understanding of partial differential equations and elaborate on the shortcomings of original scientific theories through kinetic models.