Organisers:
Zihua Guo (Monash University)
Sylvie Monniaux (University Aix-Marseille, France)

Program Description:
This workshop is dedicated to recent advances in the mathematical analysis of incompressible fluid equations, with a particular focus on situations where randomness, roughness, or dispersive and partially dissipative effects play a central role. This is a vast subject, which has been studied by mathematicians around the world for more than a century. This research programme will bring together specialists in stochastic analysis, PDE and harmonic analysis around three strongly interacting themes. Internationally recognised experts, who contributed to significant results, have already preliminarily accepted our invitation for plenary lectures. The three mentioned topics are:

• Fluid equations with noise (stochastic Navier–Stokes equations): either in the data or in the equations with issues like existence and uniqueness of solutions;
• Well-posedness and regularity for incompressible fluid equations (Navier–Stokes and Euler equations), especially in function spaces tailored to rough data and complex domains;
• Fluid models with dispersive or partially dissipative structure.

The Program intends to create a fertile ground for discussion and exchange of ideas between participants belonging to different mathematical schools and generations, inviting both promising young scholars and more experienced researchers that are experts in at least one of the above-mentioned fields. The conference programme will be developed along these lines: it will include a number of talks on “hot” topics, but will also leave room for informal discussion.

Program Structure:
TBD

Registration:

• Deadline: TBD
• Registration is by invitation only. If you are interested to participate in this program, please contact one of the organisers with your CV and research background.
• Arrival date: 27 February 2028
• Departure date: 4 March 2028

ASSOCIATED EVENTS
MATRIX Wine and Cheese Afternoon 29 February 2028
On the first Tuesday of each program, MATRIX provides a pre-dinner wine and cheese afternoon. Produce is locally-sourced to showcase delicacies from the region.