This three-year Project Grant from the National Science Foundation Division of Mathematical Sciences, under the Mathematical and Physical Sciences program (CFDA 47.049), provides $582,898 to the Regents of the University of Minnesota for research on topics in the analysis of nonlinear partial differential equations. The research focuses on fluid mechanics equations like the Navier-Stokes equations, studying well-posedness, non-uniqueness, and related problems. It also examines steady-state...
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 $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 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...
This $145,000 Project Grant awarded by the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) supports research by Florida State University (FSU) to investigate instabilities in incompressible fluid flows. The principal investigator will study new scenarios in which steady fluid flows, such as in the air, oceans, or jet engines, can become unstable due to small disturbances. This includes analyzing linear and nonlinear instabilities of the Euler...
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 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 $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,...
The National Science Foundation Division of Mathematical Sciences awarded $285,000 under the Mathematical and Physical Sciences federal grant program (CFDA 47.049) to the Regents of the University of Minnesota for a project grant titled "Critical Phenomena in Coherent Structure Formation." The grant supports research from July 15, 2022 to June 30, 2025 to develop new analytical and computational tools to systematically analyze, predict, and validate models of self-organized coherent...
This three-year, $213,000 project grant from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) will support research analyzing the effects of rotation, stratification, and dissipation in incompressible fluid flows. The awardee, Florida State University, will systematically study these mechanisms through analyzing solutions to governing equations like the rotating Navier-Stokes equations and stratified Boussinesq equations. Researchers will carry out...