Research Programs

 

Order and randomness in partial differential equations

30 August - 08 December 2023

The program focuses on three separate, yet connected, areas, Fluid motion, Integrable systems and Stochastic partial differential equations. Generally, it's impossible to solve nonlinear partial differential equations explicitly. However, certain nonlinear equations have remarkable properties which allows for explicit solutions or at least for the equations to be solved using only linear operations. These equations are called completely integrable and can be seen as generalisations of integrable systems in classical mechanics. Many examples of integrable systems appear specifically in the context of fluid mechanics and thus allows for a precise description of the fluid motion in certain cases. On the other hand, one of the hallmarks of fluid motions is turbulence, in which the fluid flow is chaotic and one can only hope to get a good grasp by studying statistical properties of the solutions rather than individual solution trajectories. The program will promote cross-fertilization between these different areas which will hopefully lead to new ideas and progress. 

Organizers
Helge Holden
NTNU - Norwegian University of Science and Technology
Thomas Kappeler
University of Zurich
Jonatan Lenells
KTH Royal Institute of Technology
Catherine Sulem
University of Toronto
Erik Wahlén
Lund University