NSF-UEFISCDI Summer School

First announcement

Location: Institute of Mathematics of the Romanian Academy (IMAR), Miron Nicolescu Amphitheater

Dates: June 30 to July 8, 2025

Support

NSF-UEFISCDI Collaboration Grant: Linear and Nonlinear Stability of Physical Flows

UEFISCDI project code ROSUA-2024-0001

Viacons Rutier, Husi with the help of Adina Ciomaga, Octav Mayer Institute of Mathematics, Iasi

"Școala Normală Superioară" Foundation

Summer School Schedule

Monday, June 30

09:20-9:30 Introduction

09:30-10:20 Vlad Vicol

10:30-11:20 Calin Martin

11:45-14:15 Welcome lunch at J'ai Bistrot Restaurant (Calea Grivitei 55)

14:30-15:20 Vlad Vicol

15:30-16:20 Calin Martin

Tuesday, July 1

09:30-10:20 Emilian Parau

10:30-11:30 Vlad Vicol

11:45-14:15 Lunch break (on your own)

14:30-15:20 Calin Martin

Wednesday, July 2

09:30-10:20 Vlad Vicol

10:30-11:20 Calin Martin

11:45-14:15 Lunch break (on your own)

14:30-15:20 Emilian Parau

Thursday, July 3

09:30-10:20 Alexandru Ionescu

10:30-11:20 Emilian Parau

11:45-14:15 Lunch break (on your own)

14:30-15:20 Lucian Beznea

Friday, July 4

10:30-11:20 Alexandru Ionescu

11:45-13:45 Lunch break (on your own)

14:00-14:50 Lucian Beznea

15:00-15:50 Lucian Beznea

Saturday, July 5

09:00-11:00 Round table discussion on Careers in Mathematics, moderated by the organizers and Lucian Beznea

11:00-13:00 Light lunch at IMAR

Monday, July 7

09:30-10:20 Emilian Parau

10:30-11:20 Alexandru Ionescu

11:45-14:15 Lunch break (on your own)

14:30-15:20 Lucian Beznea

Tuesday, July 8

09:30-10:20 Emilian Parau

10:30-11:20 Alexandru Ionescu

Titles and Abstracts

Lucian Beznea: Branching Processes Associated with Vorticity Equation

Abstract : On a bounded open set $D$ in $\R^2$, with regular boundary, following the approach of S. Benachour, B. Roynette, and P. Vallois [BeRoVa 01], we present a method of using branching processes in order to describe the time evolution of the vortexes related to a Navier-Stokes equation in the given domain $D$.
Recall that a measure-valued branching process describes the time evolution of a system of particles in $D$ and in contrast with [BeRoVa 01] we shall consider non-local branching processes, in the sense that the descendants (the new occurred vortexes) are not born from the point where the parent died.
We shall outline the construction of the branching processes with state space the set of all finite configurations of $D$ (cf. [BeLu 16] and [Li 22]) and then we shall present the application to the vorticity equation. The lectures are based on a joint work (in preparation) with Madalina Deaconu (Nancy) and Oana Lupaşcu-Stamate (Bucharest).
References:
[BeRoVa 01] S. Benachour, B. Roynette, P. Vallois, Branching process associated with 2d- Navier Stokes equation, Rev. Mat. Iberoam. 17 (2001), 331–373.
[BeLu 16] L. Beznea, O. Lupaşcu, Measure-valued discrete branching Markov processes, Trans. Amer. Math. Soc. 368 (2016), 5153–5176.
[Li 22] Li, Z., Measure-Valued Branching Markov Processes, Second Edition. Springer, 2022.

Alexandru Ionescu: On the Regularity and Stability Theory of Incompressible Flows

Abstract: Our goal in these lectures is twofold. In the first part of the course I will review the basic regularity theory of the incompressible Euler and Navier-Stokes equations in 2 and 3 dimensions, including regularity criteria, global regularity results, and the existence of weak Leray solutions. In the second part I will discuss the problem of hydrodynamic stability, focusing on recent results on the linear and nonlinear global stability of shear flows and vortices among solutions of the 2D incompressible Euler equations.

Calin Martin: Exact Solutions to the Euler Equations with a Free Surface

Abstract: In this talks, we focus on constructing exact solutions to the governing equations of geophysical fluid dynamics. These solutions, expressed in spherical coordinates, describe steady, azimuthal flows with a free surface and general fluid stratification. By applying a short-wavelength stability analysis, we demonstrate that these exact solutions are stable for certain choices of the density function. Based on joint works with D. Ionescu-Kruse (IMAR) and D. Henry (University College Cork).

Emilian Parau: Stability of Water Waves

Abstract: This minicourse will present a survey of results on the linear stability of traveling water waves. We will review nonlinear traveling wave solutions in the presence of various physical effects, including gravity, surface tension, vorticity and elasticity. To investigate their linear stability, we will introduce both asymptotic and numerical methods, including the Floquet–Fourier–Hill approach. The classical Benjamin–Feir (or modulational) instability will also be discussed.

Vlad Vicol: Anomalous Diffusion in Passive Scalars

Abstract: The goal of these lectures is to construct a class of incompressible vector fields that have many of the properties observed in a fully turbulent velocity field, and for which the associated scalar advection-diffusion equation generically displays anomalous diffusion. We also propose an analytical framework to study anomalous diffusion via a backward cascade of renormalized eddy viscosities. Our proof is by “fractal” homogenization, that is, we perform a cascade of homogenizations across arbitrarily many length scales.

Participants

Ataleshvara Bhargava, Purdue University, PhD student
Ștefan Bîrcă, University of Bucharest, BSc student
Francisc Bozgan, New York University Abu Dhabi, PostDoc
Gabriel Brehuescu, Alexandru Ioan Cuza University, Iasi, MSc student
Adelina Calina, University of Bucharest, PhD student
Ciro Campolina, Scuola Normale Superiore di Pisa, PostDoc
Andrei Cațaron, University of Bucharest, PhD student
Diana-Maria Ciotir, Alexandru Ioan Cuza University, Iasi, MSc student
Adrian-Constantin Culică, Alexandru Ioan Cuza University, Iasi, MSc student
Andreea Dima, IMAR, PhD student
Nicoleta Dumitru, University of Bucharest, PhD student
Cristina Gheorghe, Babeș-Bolyai University, Cluj, PhD student
Nicholas Gismondi, Purdue University, PhD student
Yuqi Li, Bielefeld University, PhD student
Paula Luna Velasco, University of Sevilla, PhD student
Gabriel Majeri, University of Bucharest, PhD student
Dragos Manea, IMAR, PhD student
Claudiu Mîndrilă, BCAM Bilbao, Spain, PostDoc
Radu Ordean, University of Bucharest, PhD student
Josh Payne, University of Bath, PhD student
Georgiana Prisacaru, University of Bucharest, BSc student
Christian Puntini, University of Vienna, PhD student
Alex Radu, IMAR, PhD student
Teodor Rugină, University of Bucharest, PhD student
Anisia Teca, University of Craiova, PhD student
Anda Toma, University of Bucharest, MSc student
Claudia Pena Vasquez, BCAM Bilbao, Spain, PhD student