With applications ranging from the study of biological processes, aerodynamics, and meteorology, fluid dynamics remains one of the most important fields of classical and modern physics. Despite the importance of fluids to virtually all life, little is known about how to predict fluid motion in general settings. The goal of this project is to advance our knowledge of some of the fundamental questions regarding fluid flow: are the laws of classical physics sufficient to provide a complete picture of fluid flow in all scenarios? More precisely, are there extreme events in which the classical laws governing fluid motion break down? If so, is there a way to amend the classical laws to give effective models of fluid motion in such circumstances? This award also supports the involvement of a postdoctoral scholar and a graduate student in the research project.

Mathematically, these questions relate to the question of the global solvability for the classical fluid equations: the Euler and Navier-Stokes equations. The focus of this work will be on the problem of singularity formation for the Euler equation. We will analyze the stability of recently constructed examples of singularity formation and study the extent to which these examples can be extended to give singularity formation for more regular solutions. In parallel, we will consider the problem of enhanced dissipation and study the effects of possible singular behavior in inviscid problems on rapid dissipation in viscous problems.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

Agency
National Science Foundation (NSF)
Institute
Division of Mathematical Sciences (DMS)
Application #
1945669
Program Officer
Pedro Embid
Project Start
Project End
Budget Start
2020-08-01
Budget End
2020-09-30
Support Year
Fiscal Year
2019
Total Cost
$23,252
Indirect Cost
Name
University of California San Diego
Department
Type
DUNS #
City
La Jolla
State
CA
Country
United States
Zip Code
92093