This Project Grant award of $302,028.00 from the National Science Foundation's (NSF) Mathematical and Physical Sciences Federal Grant Program (CFDA 47.049) supports fundamental research on nonlinear hyperbolic and dispersive partial differential equations (PDEs). The award aims to deepen the understanding of these PDEs, which are critical for describing natural phenomena across scales, by investigating long-term dynamics, singularity formation, and the stability of special solutions. Key...
The National Science Foundation awarded The Johns Hopkins University a $320,648 Project Grant under the Mathematical and Physical Sciences program (CFDA 47.049). The grant will support research into various aspects of the theory of partial differential equations as they relate to the dichotomy between regularity and singularity formation. The Principal Investigator will pursue research in regularity theory and geometric properties for partial differential equations arising in the theory of...
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 Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) provides $300,000.00 to the University of Maryland, College Park to advance research across three classes of nonlinear partial differential equations. The project aims to study emergent phenomena, conservation laws, and the pressure-less early universe model in multiple spatial dimensions. Key focus areas include Euler alignment, nonlinear conservation laws, and the...
This Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) supports fundamental research on dispersive and wave equations, and their applications in physics and science. The $176,355 award to the University of Chicago, made on May 15, 2025, funds five research projects (A-E) investigating mathematical theory of wave turbulence, Gibbs measures in statistical physics and quantum field theory, and related interdisciplinary areas....
This National Science Foundation project grant of $428,169 supports research in harmonic analysis and partial differential equations at the University of Illinois from August 2022 through July 2025. The award is funded through the Mathematical and Physical Sciences program (CFDA 47.049). The project involves foundational research in harmonic analysis and analysis of partial differential equations with a focus on long-time dynamical properties and decay estimates. Specific areas of study...
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 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 Project Grant from the National Science Foundation (NSF) under the Mathematical and Physical Sciences program (CFDA 47.049) provides $179,538 to Wake Forest University from July 1, 2022 to December 31, 2022. The university will use the funding to further mathematical study of dispersive and diffusive partial differential equations on bounded intervals and the half line. Researchers will apply the Uniform Transform Method to extend previous results on unbounded domains to bounded intervals...
This Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) supports research into harmonic analysis and the behavior of quantum waves on curved spaces, particularly the Schrödinger equation. The $215,830 award to Louisiana State University, effective July 1, 2025 through June 30, 2028, will fund the development of new mathematical tools to study wave behavior and derive space-time estimates for the linear Schrödinger equation...