This workshop focuses on recent advancements in evolutionary PDEs and control theory, with particular emphasis on conservation laws and their applications across mathematics and science. Inspired by Alberto Bressan's groundbreaking contributions, the event will explore cutting-edge developments in hyperbolic conservation laws, fluid dynamics, and control theory. Topics include mixing in incompressible fluids, convex integration for Euler equations, energy equality in Navier-Stokes equations, and singular limits in fluid dynamics models. The workshop will also address the theory of control and its applications to real-world problems such as traffic management, resource distribution, and environmental challenges. By bringing together experts in these fields, the workshop aims to stimulate discussion on new mathematical techniques and foster interdisciplinary collaborations, paving the way for future breakthroughs in both theoretical and applied domains.
The workshop aims to present fundamental theoretical advances and the most promising research directions in evolutionary PDEs and control theory. The focus will be particularly on challenging problems arising in the analysis of conservation laws and control theory, and their applications in related areas of mathematics and science. Alberto Bressan's contributions to these fields have been fundamental, often reshaping the research area by solving open problems, introducing completely new techniques, and generating new research directions.
The fundamental progress achieved in recent years by the mathematical theory of hyperbolic conservation laws and fluid dynamics (both classical and non-classical) has opened the door to a host of further advances in theoretical aspects and applications, as well as new research trends originating from surprising and deep connections between nonlinear hyperbolic PDEs and other branches of analysis.
Topics of these achievements include:
- Mixing of incompressible fluids and well-posedness of transport equations for nearly incompressible vector fields
- Convex integration for Euler equations and Magnetohydrodynamics
- Energy equality for the Navier-Stokes equations
- Stability/instability of shear flows for hydrostatic Euler equations
- Transport of vortex points/sheets in fluids
- Singular limits for fluid dynamics models
- Surface waves on the plasma-vacuum interface
- Compactness, regularity, and Lagrangian representation of solutions to hyperbolic conservation laws, possibly in the presence of local or non-local source terms
- Well-posedness of conservation laws in granular flow models
The theory of control provides efficient solutions to many critical real-life problems (such as urban traffic management, traffic networks, smarter cities challenges, waterways or gas pipeline distribution, cost-efficient production lines, control of invasive species, and fire spreading) and constitutes a rich, mostly still unexplored branch of mathematics. Refined mathematical techniques are required to address these problems, e.g., the differential structure and Pontryagin-type necessary conditions for optimality, the controllability of ODEs and evolution equations, and Lagrangian-type approaches to optimality.
15-19/06/2026 @ Università degli Studi di Padova, Dipartimento di Matematica ``Tullio Levi-Civita’’
Preliminary:
Amadori Debora (UNIVAQ)
Ambrosio Luigi (SNS Pisa)
Cannarsa Piermarco (Roma2)
Chiri Maria Teresa (Queen's)
Coclite Giuseppe (POLIBA)
Colombo Rinaldo M. (UNIBS)
Constantin Adrian (Wien)
Coron Jean-Michel (UPMC)
Dafermos Constantine (Brown)
Donatello Carlotta (Franche-Comté)
Glass Oliver (Dauphine)
Goatin Paola (Inria)
Guerra Graziano (Milano Bicocca)
Holden Helge (NTNU)
Lewicka Marta (Pittsburgh)
Marcati Pierangelo (GSSI)
Marchini Elsa (POLIMI)
Mazzola Marco (Jussieu)
Nguyen Tien Khai (NCSU)
Palladino Michele (UNIVAQ)
Piccoli Benedetto (Rutgers)
Giovanni Colombo (Padova)
Serre Denis (ENS Lyon)
Shen Wen (PennState)
Amadori Debora (UNIVAQ)
Ambrosio Luigi (SNS Pisa)
Cannarsa Piermarco (Roma2)
Chiri Maria Teresa (Queen's)
Coclite Giuseppe (POLIBA)
Colombo Rinaldo M. (UNIBS)
Constantin Adrian (Wien)
Coron Jean-Michel (UPMC)
Dafermos Constantine (Brown)
Donatello Carlotta (Franche-Comté)
Glass Oliver (Dauphine)
Goatin Paola (Inria)
Guerra Graziano (Milano Bicocca)
Holden Helge (NTNU)
Lewicka Marta (Pittsburgh)
Marcati Pierangelo (GSSI)
Marchini Elsa (POLIMI)
Mazzola Marco (Jussieu)
Nguyen Tien Khai (NCSU)
Palladino Michele (UNIVAQ)
Piccoli Benedetto (Rutgers)
Serre Denis (ENS Lyon)
Shen Wen (PennState)
Franco Rampazzo (Padova)
Vinter Richard (Imperial)
FabioAncona (UNIPD), StefanoBianchini (SISSA-Trieste), PaoloBonicatto (UNITN), LauraCaravenna (UNIPD), GuidoDePhilippis (UNIPD), DonatellaDonatelli (UNIVAQ), ElioMarconi (UNIPD)
