Project Grant 2245021
- 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...
- 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...
- This Project Grant award from the National Science Foundation (CFDA 47.049 - Mathematical and Physical Sciences) provides $608,098 to The Trustees of Princeton University to conduct collaborative research on understanding singularities in incompressible fluid flows. The three-year project (July 1, 2023 to June 30, 2026) integrates theoretical proofs, numerical analysis, and machine learning to investigate the formation of singularities in three-dimensional incompressible Navier-Stokes and...
- 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 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...
- This three-year National Science Foundation Project Grant of $197,999 supports research and education activities at Worcester Polytechnic Institute under the Mathematical and Physical Sciences program (CFDA 47.049). The award will fund the development of novel mathematical methods to analyze partial differential equations describing singularities in continuum mechanics and materials science systems. The principal investigator will extend differential inclusion theory on rigidity and flexibility,...
- This federal Project Grant award from the National Science Foundation (CFDA 47.049 - Mathematical and Physical Sciences) provides $159,956 to New York University (NYU) to investigate the potential breakdown mechanism for various fluid dynamics equations, including the incompressible 3D Euler equations. The research aims to determine whether these equations can develop a finite-time singularity from a smooth initial condition with finite energy. The project builds on the principal...
- Federal Project Grant Award Summary The National Science Foundation's Division of Mathematical Sciences (CFDA 47.049, Mathematical and Physical Sciences program) awarded a $300,000 Project Grant to the California Institute of Technology for a two-year project period (September 1, 2025 – August 31, 2027) to investigate potential finite-time singularities in the three-dimensional incompressible Navier-Stokes equations. The research develops a novel mathematical and computational approach to...
- This $432,460 National Science Foundation project grant supports research at Brown University from June 2022 to May 2025 under the Mathematical and Physical Sciences program (CFDA 47.049). The research aims to advance the theory of singular integrals in non-smooth settings through consideration of weighted norm estimates, spectral theory, and dimension reduction techniques. Specifically, the project will characterize boundedness for singular operators on graphs and matrices, address the...
- The National Science Foundation (NSF) Division of Mathematical Sciences awarded a $399,998 Project Grant to the Massachusetts Institute of Technology (MIT) under the Mathematical and Physical Sciences program (CFDA 47.049) to fund research on singularities and rigidity in geometric evolution equations. The research focuses on geometric flows, which model the evolution of geometric objects like functions, surfaces, or Riemannian metrics over time using nonlinear generalizations of the classical...
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; formation of singularities for solutions to the three-dimensional Euler equations; and optimization of physics-informed neural networks. Students, postdoctoral fellows, and visitors will participate in collaborative activities, including annual workshops at investigator institutions to disseminate research progress and training opportunities. Additionally, the investigators will organize a summer school at Princeton University for graduate students and advanced undergraduates featuring scientific minicourses and career mentoring panels.
Mod # | Description | ReasonForModification | Federal Obligation | Date |
|---|---|---|---|---|
| Not listed | $265.8k | 3/17/23 |