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 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 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 $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 (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 $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...
This Project Grant award of $300,000.00 from the National Science Foundation's (NSF) Division of Mathematical Sciences supports research to develop new mathematical methods and techniques for analyzing multi-dimensional partial differential equations (PDEs) that govern fluid flows and related phenomena. The research project, titled "Analysis of Hyperbolic and Mixed-Type PDEs in Conservation Laws and Applications," aims to advance the mathematical understanding of multi-dimensional...
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,...
This $270,000 Project Grant award, provided by the National Science Foundation (NSF) under the Mathematical and Physical Sciences (CFDA 47.049) program, will support two research programs related to the mathematical theory of fluids, gases, and plasmas. The first program will examine non-uniqueness phenomena and instability in nonlinear partial differential equations, particularly those used in modeling incompressible fluid mechanics. The second program will investigate the structure of shock...
This Project Grant award from the National Science Foundation (NSF) Mathematical and Physical Sciences (MPS) program, CFDA 47.049, provides $167,711 to the Research Foundation of the City University of New York (RFCUNY) - Brooklyn College to conduct research on the dynamics of fluids with singular interfaces. The project aims to develop new mathematical tools to study free-surface fluid flows, with a focus on understanding plasma confinement in fusion energy and the long-term behavior of...