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 $100,972 federal Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences Program (CFDA 47.049) supports fundamental research on nonlinear partial differential equations and their applications in fields such as crystal growth, combustion, and game theory. The primary investigator (PI) will study the regularity, large-time behavior, and qualitative properties of solutions to these equations, which have connections to areas like the calculus of...
This Project Grant award from the National Science Foundation (NSF) Division of Mathematical Sciences (CFDA 47.049 - Mathematical and Physical Sciences) supports research focused on addressing fundamental questions in partial differential equations and optimization theory. The $291,367 award, spanning July 2024 to June 2027, will advance the Principal Investigator's work on characterizing extremal functions for Morrey's inequality, studying solutions to the pressureless Euler system, and...
This Project Grant from the National Science Foundation's Mathematical and Physical Sciences program (CFDA 47.049) provides $232,812 to The Johns Hopkins University from July 1, 2022 to June 30, 2025 to improve understanding of dispersive partial differential equations. Key products include research on the long-time behavior of solutions to critical scaling equations like the Schrödinger maps problem and focusing/mass-critical nonlinear Schrödinger equation. Additional work will analyze energy...
This Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences (CFDA 47.049) program is supporting research by The Trustees of Columbia University in the City of New York to advance the theoretical understanding of partial differential equations, free boundary problems, and related mathematical concepts. The $273,927 award, with a performance period from July 1, 2024 to June 30, 2027, focuses on developing new methods and regularity theories for specific...
The National Science Foundation awarded a $150,193 Project Grant to the University of South Carolina under the Mathematical and Physical Sciences program (CFDA 47.049). The grant will support research into non-local partial differential equations in collective dynamics and fluid flow from August 1, 2023 through July 31, 2028. Specifically, the university will study three families of partial differential equations with non-local structures to model collective behavior and fluid dynamics....
This $234,951 federal Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) supports research into nonlinear partial differential equations and minimal submanifolds in Lagrangian geometry. The project, conducted by the University of North Carolina at Chapel Hill, will generate research opportunities for graduate students and facilitate the mentoring of graduate students and postdocs. The research will focus on two key areas:...
This National Science Foundation (NSF) Project Grant award provides $253,734 to The Johns Hopkins University to support research on the regularity of solutions to elliptic partial differential equations and generalized minimal submanifolds. The award focuses on two main mathematical objectives: studying unique continuation for solutions to elliptic PDEs and investigating the regularity theory for generalized minimal submanifolds. This research under the NSF's Mathematical and Physical Sciences...
This $300,000 federal Project Grant awarded by the National Science Foundation (NSF) under the Mathematical and Physical Sciences (CFDA 47.049) program supports fundamental mathematical and computational research on complex stochastic systems with infinite degrees of freedom. The project aims to develop new theoretical frameworks and analytical techniques for studying the asymptotic behavior of stochastic partial differential equations (SPDEs) with multiple scales and conservation laws. The...
This Project Grant award, totaling $150,000.00, was provided by the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) to support research on asymptotic phenomena in partial differential equations (PDEs) arising in various scientific applications. The principal investigator will investigate the long-time behavior of solutions to reaction-diffusion equations in heterogeneous and random environments, study the long-time and white-noise limits of physically...