This $325,249 three-year Project Grant from the National Science Foundation's Mathematical and Physical Sciences program will support collaborative research into singularities in incompressible flows. The grantee, Brown University, will partner with other leading research universities to integrate theoretical proofs, numerical analysis, and machine learning to further understanding of whether three-dimensional incompressible flows develop singularities in finite time and whether solutions to the...
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 $265,813 National Science Foundation project grant supports collaborative research on singularities in incompressible flows through computer-assisted proofs and physics-informed neural networks. Funded under the Mathematical and Physical Sciences program (CFDA 47.049), the award brings together five principal investigators from leading U.S. research universities to investigate three specific projects: non-uniqueness of Leray-Hopf solutions to the Navier-Stokes equations in three dimensions;...
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 $138,009 federal Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences (CFDA 47.049) program supports a collaborative research project at New York University (NYU) on the fundamental problems of singularities in 3D incompressible fluid flows and Navier-Stokes equations. The project integrates theoretical mathematical analysis, numerical simulations, and machine learning techniques to advance understanding of fluid flow singularities. The five...
The National Science Foundation (NSF) awarded a $689,835 Project Grant under its Mathematical and Physical Sciences (CFDA 47.049) program to Brown University. The grant, with a performance period from December 1, 2024 to November 30, 2027, supports research focused on developing machine learning approaches for solving long-standing open problems in nonlinear partial differential equations, including dispersive, elliptic, and geometric frameworks. The project aims to unlock new mathematical...
This National Science Foundation (NSF) Project Grant award, provided under the Mathematical and Physical Sciences program (CFDA 47.049), supports research focused on understanding regular and singular incompressible fluid flows. The $300,000 award, granted from August 1, 2024 to July 31, 2027, aims to advance the mathematical understanding of solutions to the incompressible Navier-Stokes and Euler equations, particularly in the areas of regularity, uniqueness, and stability. The project...
Brown University received a $400,000 Project Grant award from the National Science Foundation Division of Mathematical Sciences under the Mathematical and Physical Sciences program (CFDA 47.049). The award will fund research from July 1, 2023 through June 30, 2026 to develop efficient numerical methods for solving partial differential equations. Specifically, Brown University researchers will investigate algorithm development, analysis and application of high-order numerical methods including...
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...
Brown University received a $343,614 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 will fund research and training from July 2023 through June 2026 related to developing provably stable higher-order splitting methods for fluid-structure interaction problems involving coupled partial differential equations. One graduate student will receive training on multi-physics...