This Project Grant award for $257,457 from the National Science Foundation (NSF) Division of Mathematical Sciences supports research by the University of Alabama at Birmingham (UAB) to investigate three key problems in fluid mechanics. The overarching objective is to utilize a novel mathematical framework developed by the Principal Investigator to study the spatial intermittency of turbulent flows, which is critical for understanding phenomena like vortex structures in turbulence. The three...
This $204,884 Project Grant award from the National Science Foundation (NSF) Directorate for Mathematical and Physical Sciences (CFDA 47.049) supports research by Towson University to study various subgrid scale turbulence models and their connections to the Navier-Stokes equations. The research aims to explore the mathematical properties of these turbulence models, apply data assimilation algorithms, and leverage deep learning methods for parameter estimation. Key focus areas include...
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...
The National Science Foundation Division of Mathematical Sciences awarded a $198,055 Project Grant to the Georgia Tech Research Corporation from September 1, 2023 through August 31, 2028 under the Mathematical and Physical Sciences federal grant program (CFDA 47.049). The award will support research investigating chaotic dynamics in dynamical systems with noise, and applying tools from smooth ergodic theory and probability theory to rigorously analyze chaotic behavior in practical systems....
This five-year $154,264 Project Grant from the National Science Foundation's Mathematical and Physical Sciences program (CFDA 47.049) supports research and educational activities at Drexel University related to uncertainty quantification, long-time statistics, and singularity formation in fluid flow models. The Principal Investigator will address topics including parameter recovery from sparse noisy observations using Bayesian inverse problems and Markov chain Monte Carlo algorithms applied to...
This $339,994 Project Grant awarded by the National Science Foundation's (NSF) Mathematical and Physical Sciences program supports research to advance the fundamental theoretical understanding of wave turbulence in the atmosphere and oceans. The award to New York University (NYU) will fund a multi-pronged effort combining theory and numerical modeling in three key areas: 1) investigating how broadband wave spectra can emerge from monochromatic wave sources through interactions with mean...
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 Project Grant award, valued at $300,000.00 and effective from July 1, 2025 to June 30, 2028, was provided by the National Science Foundation (NSF) under the Mathematical and Physical Sciences (CFDA 47.049) federal grant program. The award supports research focused on three main areas: the formation of singularities in incompressible fluids, the study of steady solutions to the incompressible Euler equation in two and three dimensions, and the phenomenon of fluid mixing. The primary...
The National Science Foundation awarded a $360,000 Project Grant to the University of Illinois for the project "Pathological Solutions of Fluid Equations". The grant period runs from June 1, 2023 to May 31, 2026. The project will study fundamental open questions concerning the equations of fluid motion, which are widely used in physics and engineering applications. The research aims to demonstrate limitations in the notion of "weak solutions" to these equations, which have...
This $300,000 Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) supports research by the California Institute of Technology (Caltech) to study potential singularities in the Navier-Stokes equations. The Navier-Stokes equations describe fluid motion and are fundamental to science and engineering, but key theoretical questions remain unanswered. The research aims to develop new mathematical and computational approaches to...