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 $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 $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 from the National Science Foundation (NSF) Mathematical and Physical Sciences (CFDA 47.049) program provides $257,048 to New York University (NYU) to conduct research on singularities in fluids. The key focus areas include: Providing a full description of shock wave formation and development for multi-dimensional compressible Euler equations. Further developing prior work on self-similar imploding solutions for isentropic compressible flows to investigate new types of...
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 $300,000 Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) supports research by Duke University into fundamental aspects of the dynamics of incompressible fluids. The research project spans three main directions: investigating the formation of singularities in incompressible fluids, studying steady solutions to the incompressible Euler equation, and examining the phenomenon of fluid mixing. The project aims to advance...
This Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences Program (CFDA 47.049) provides $300,000.00 in funding to the California Institute of Technology (Caltech) to study potential singularities in the Navier-Stokes equations, which describe the motion of fluids. The research aims to develop a new mathematical and computational approach to uncover mechanisms that could lead to singularity formation in the 3D Navier-Stokes equations. This work is...
The National Science Foundation (NSF) awarded a $299,213 Project Grant under the Mathematical and Physical Sciences (CFDA 47.049) federal grant program to The Trustees of Princeton University to study the dynamics and stability of solutions to important partial differential equations that describe classical systems in applied mathematics and physics, such as incompressible fluids, geophysical flows, plasma, and water waves. The 3-year award, effective July 1, 2024, will establish...
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...
The Trustees of Princeton University were awarded a $500,000 Project Grant from the National Science Foundation Division of Mathematical Sciences on August 15, 2021. The grant supports research titled "Symmetry, Singularity, and Stability in Fluids and Plasmas" to be conducted at Princeton University in Princeton, New Jersey through July 31, 2025. This award falls under the Mathematical and Physical Sciences program (CFDA 47.049) of the National Science Foundation, which aims to...