Project Grant 2531744
- This three-year, $226,333 Project Grant from the National Science Foundation's Mathematical and Physical Sciences program (CFDA 47.049) supports research at Brown University on computer-assisted proofs in fluid mechanics and applications. The award will advance methods for pursuing singularities or global existence in incompressible fluids, and apply techniques to long-standing problems in spectral geometry and mathematical physics. Researchers will utilize numerical computations,...
- This Project Grant award of $150,000.00 from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) supports research into the asymptotic behavior of partial differential equations (PDEs) across a range of scientific applications. The Principal Investigator (PI) will investigate long-term propagation and front structure in reaction-diffusion equations, analyze limits of stochastic PDEs in physical systems, and study the effects of viscosity on shock...
- The National Science Foundation's (NSF) Integrative Activities (IA) program, Assistance Listing 47.083, has awarded a $160,000 Project Grant to Brown University to conduct research on partial differential equations (PDEs) commonly encountered in physics and engineering. The project, running from July 1, 2024 to June 30, 2027, will focus on developing new methods to study elliptic PDE equations in composite materials, explore the regularity of solutions to the one-phase Muskat problem in fluid...
- This federal Project Grant award in the amount of $300,000.00 from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) advances the understanding of nonlinear dispersive partial differential equations (PDEs), which serve as mathematical models for wave phenomena in diverse scientific domains. The research focuses on exploring fundamental questions related to the formation, stability, and interaction of coherent structures like solitons, vortices,...
- This $300,000 Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) supports fundamental research aimed at advancing the mathematical analysis of nonlinear partial differential equations. The research has three main focus areas: (1) studying fluid dynamics problems with free boundaries, such as water waves, tsunamis, and hurricanes; (2) investigating the dynamics of gases and plasmas under physical kinetic boundary conditions,...
- This Project Grant award of $311,106 from the National Science Foundation's (NSF) Mathematical and Physical Sciences (CFDA 47.049) program supports research by Brown University on several important mathematical problems in physics, fluid dynamics, and general relativity. The key research objectives include: Studying the "ghost effect" in heat conduction and constructing dynamical stability for related kinetic models. Developing global solutions for fundamental plasma physics models...
- This Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) provides $300,000 to Brown University to advance the understanding of nonlinear dispersive partial differential equations (PDEs). The research explores fundamental questions in the analysis of nonlinear dispersive systems, with a focus on the formation and long-time dynamics of coherent structures such as solitons, vortices, and singularities in contexts where...
- This Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) in the amount of $252,563 supports research on several nonlinear partial differential equations with important applications in science, economics, engineering, meteorology, and physics. Specifically, the project investigates "singular higher-order linearized Monge-Ampère type equations with drifts" which have connections to areas like analysis, geometry,...
- This Project Grant award, valued at $220,000.00, was provided by the National Science Foundation (NSF) under the Mathematical and Physical Sciences (CFDA 47.049) federal grant program. The award supports research by Brown University to study variational methods in singular geometry, with applications to phenomena like classical mechanics, geodesics, and harmonic maps. The project aims to develop new analytical techniques to investigate the properties of solutions to non-linear elliptic PDEs, and...
- 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....
This Project Grant award, funded by the National Science Foundation's (NSF) Integrative Activities program (CFDA 47.083), provides $234,669.00 to the University of Nebraska-Lincoln to support a research fellowship for an assistant professor and training for a graduate student. The project, conducted in collaboration with Brown University, will focus on mathematical analysis of prominent partial differential equations in fluid mechanics and mathematical physics. Specifically, the principal investigator will seek to prove the uniqueness of weak solutions to the Cahn-Hilliard equation and develop a global solution theory for the surface quasi-geostrophic equation with stochastic forcing. The graduate student will gain exposure to cutting-edge research and networking opportunities at Brown University. Additionally, the principal investigator will receive mentorship in research collaboration, student/postdoctoral supervision, and academic service. This project aims to advance the fundamental understanding of mathematical models used to describe real-world phenomena, with the potential to contribute to more reliable predictions in fields like fluid dynamics.
Mod # | Description | ReasonForModification | Federal Obligation | Date |
|---|---|---|---|---|
| Not listed | $234.7k | 9/15/25 |