The National Science Foundation Division of Mathematical Sciences awarded Brown University a $401,152 Project Grant under the Mathematical and Physical Sciences federal grant program (CFDA 47.049) to develop Hamiltonian methods for modeling dispersive fluids and plasmas. Over the three-year period from July 2022 to June 2025, Brown University researchers will conduct qualitative and quantitative studies of partial differential equations describing fluid motions in galaxies, gases, and plasmas. They will analyze the asymptotic behavior and stability of various equilibria, leveraging dispersion as a stabilizing mechanism. The researchers will also study the effect of rotation on fluids and its mathematical expression. The project aims to better understand phenomena like Landau damping and will consider models of non-equilibrium distributions. It seeks to prove stability of solutions through decomposition techniques and normal form methods. Insights gained from this research could enhance understanding of major astrophysical and plasma problems.
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