Displaying items by tag: ASPIRE

 I have been awarded a grant from the Office of the Vice President for Research at the University of South Carolina, on a one-year project: Transition between inviscid and viscous primitive equations.

Project Summary

The primitive equations are the fundamental mathematical models governing large-scale atmospheric and oceanic dynamics. They arise from the Navier-Stokes equations under the hydrostatic approximation and form the core of modern climate and weather models. Despite their central role, the mathematical behavior of the primitive equations depends sensitively on the strength and structure of viscosity, and transitions between well-posed and ill-posed regimes remain poorly understood.

This project investigates the transition between inviscid and viscous primitive equations using fractional horizontal dissipation, which provides a continuous interpolation between these regimes. Recent joint work by the PI established the first rigorous results in two dimensions, identifying a sharp threshold separating local well-posedness from ill-posedness and proving global regularity in certain subcritical regimes. However, the underlying transition mechanisms and their robustness remain largely unexplored.

The proposed research aims to extend this framework in three directions:
(1) resolving the open transition regime between local and global regularity,
(2) understanding the effect of vertical viscosity, and
(3) initiating the study of three-dimensional models, where new mechanisms such as vorticity stretching arise.

The project will develop analytical tools that clarify how viscosity stabilizes geophysical flows, produce publishable results, and lay the groundwork for external funding applications to NSF-DMS and related programs.

USC Office of Research Awards Announcement Page

I am honored to be named a 2025 McCausland Faculty Fellow.

About the Fellowship

The McCausland Faculty Fellowship is the premier faculty fellowship program in the McCausland College of Arts and Sciences. It supports early-career McCausland College of Arts and Sciences faculty who are committed, creative teachers and rising stars in their academic disciplines.

The college established the program with a $10 million endowment from alumnus Peter McCausland (’71 history) and his wife, Bonnie. Through this fellowship, the McCauslands support innovative research and teaching, enhancing the career of faculty and the experience of students in the University of South Carolina's largest college.

Announcement from College of Arts and Sciences

I have been awarded a grant from the Office of the Vice President for Research at the University of South Carolina, on a one-year project: Multiscale nonlocal models in traffic flows.

Project Summary

Mathematical models on traffic flows have been studied extensively in the past century. Many celebrated models lie in a beautiful multiscale framework. The investigations on these models play an important role in designing traffic networks and preventing traffic jams.

Recently, the fast development of self-driving vehicles and new communication technologies allow long-range interactions in traffic networks. It attracts a lot of interest in nonlocal traffic flow models.

The aim of the proposed project is to develop the mathematical theory on non-local traffic flows and understand how nonlocal interactions can help to optimize the traffic networks and avoid the creation of traffic congestions.

The PI has been actively working on a variety of multiscale nonlocal models in physical, biological, and sociological contexts. These experiences can greatly help the understanding of the nonlocal phenomena in traffic models. Preliminary investigations show intriguing behaviors and promising outcomes. Results generated from this project will be capitalized to prepare proposals for external grants from NSF and DOT.

UofSC Office of Research Awards Announcement Page