Abstract
The main goal of the project is to study the dynamics of solutions of several important partial differential equations, which describe classical systems such as incompressible fluids, geophysical flows, plasma, and water waves.
The PIs will investigate the long-time dynamics of solutions of several evolution PDE, such as the Euler and the Navier-Stokes equations, geophysical flows, the Vlasov-Poisson system, and water waves models, mainly in dimensions 2 and 3. These equations have important explicit solutions, and the main questions to be considered have to do with the long-time stability of these solutions. Specific major problems will be investigated, concerning the global stability of shear flows and vortices for the 2D Euler and Navier-Stokes equations, the instability of mountain waves, the complex dynamics of oceanic flows, and the global stability of homogeneous solutions of the Vlasov-Poisson system. This is a very active field, with many recent methods and results. It is likely that other important problems will emerge and will become feasible during the course of the investigation.
The project will establish links and collaborations between researchers at leading American and Romanian universities, as part of the new NSF-UEFISCDI initiative, support the training and development of early-career researchers and students, and disseminate the research widely at conferences and summer schools.
Team Members
Liviu Ignat, Senior Researcher I, Institute of Mathematics of the Romanian Academy
Alexandru Ionescu, Professor of Mathematics, Princeton University (Principal Investigator NSF)
Delia Ionescu-Kruse, Senior Researcher I, Institute of Mathematics of the Romanian Academy (Principal Investigator UEFISCDI)
Sergiu Moroianu, Professor, University of Bucharest and Institute of Mathematics of the Romanian Academy
Graduate Students
Adelina Calina, Graduate Student, University of Bucharest
Alexandru Radu, Graduate Student, Institute of Mathematics of the Romanian Academy
Noah Stevenson, Graduate Student, Princeton University
Publications
L. I. Ignat and E. Zuazua, Optimal convergence rates for the finite element approximation of the Sobolev constant. Preprint (2025), arXiv:2504.09637
L. I. Ignat and E. Zuazua, Sharp numerical approximation of the Hardy constant. Preprint (2025), arXiv:2506.19422
A. D. Ionescu, B. Pausader, X. Wang, and K. Widmayer, Nonlinear Landau damping and wave operators in sharp Gevrey spaces. Preprint (2024), arXiv:2405.04473.
Conferences
NSF-UEFISCDI Summer School at the Institute of Mathematics of the Romanian Academy, June 30 - July 8, 2025