The National Science Foundation Division of Mathematical Sciences awarded Indiana University a $235,718 Project Grant under the Mathematical and Physical Sciences federal grant program (CFDA 47.049). The grant will support research investigating open questions in nonlinear time-asymptotic stability of discontinuous inviscid periodic waves and multi-dimensional hydraulic shocks, invariant manifolds for steady Boltzmann's equation, and bifurcation and stability of Turing patterns in...
This Project Grant award for $300,000 from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) supports fundamental research on the stability and behavior of large-amplitude relaxation waves in shallow water flow and other physical systems. The principal investigator will study key open problems related to the nonlinear time-asymptotic stability of discontinuous periodic waves and multidimensional hydraulic shocks, with the goal of developing new...
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...
The National Science Foundation (NSF) awarded a $299,213 Project Grant under the Mathematical and Physical Sciences (CFDA 47.049) federal grant program to The Trustees of Princeton University to study the dynamics and stability of solutions to important partial differential equations that describe classical systems in applied mathematics and physics, such as incompressible fluids, geophysical flows, plasma, and water waves. The 3-year award, effective July 1, 2024, will establish...
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 three-year National Science Foundation Project Grant of $168,087 will support research into nonlinear wave models in bounded domains. The principal investigator and their team at the University of Kansas Center for Research will develop a methodology for analyzing the behavior of dispersive equations modeling optical and water wave phenomena in confined regions. They will provide tools to understand novel behaviors and design physical and numerical experiments. Three research components are...
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 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...
The University of Michigan will receive $810,746 under a Project Grant from the National Science Foundation's Mathematical and Physical Sciences program (CFDA 47.049) to conduct research on mathematical modeling of fluid free boundary problems. Specifically, researchers will develop mathematical tools to analyze the long-term behavior of water waves in two and three dimensions, with and without surface tension, as well as the interaction of ocean waves with rigid coastal boundaries. The...
The National Science Foundation (NSF) awarded a $450,000 Project Grant to the University of California, Merced to conduct a hybrid experimental and numerical study of vortex mechanics. The goal is to develop new vortex models that incorporate features like internal vortex structure and coupling to other flows, in order to improve prediction and control of fluid behavior in a wide range of contexts. This 3-year project will validate the new vortex models through experiments on streamwise vortices...