The National Science Foundation (NSF) awarded a $186,811 project grant under the Mathematical and Physical Sciences (CFDA 47.049) program to Georgetown University for the project "Analytical Challenges Near Dynamical Thresholds for Nonlinear Wave and Fluid Equations". The project seeks to understand solutions to partial differential equations that live on the verge of different dynamical regimes, with the goal of elucidating the limitations and appropriate uses of these mathematical models in describing physical systems. The research will leverage tools from real and harmonic analysis, spectral theory, and dynamical systems to investigate three distinct problems related to integrable PDEs, wave turbulence models, and vortex filaments. In addition to the research goals, the project includes educational and outreach activities to train graduate and undergraduate students. The project will be conducted at Georgetown University and is scheduled for completion by August 31, 2027.
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