Fluid mechanics has numerous real-world applications, e.g. weather prediction, industry, and agriculture. Modeling and analyzing the motion of fluids through partial differential equations (PDEs) have been studied for centuries by physicists, mathematicians,  and engineers. Mathematical analysis on such nonlinear PDEs is a notoriously difficult research direction. However, it has recently seen significant developments due to multiple breakthroughs in the areas of nonuniqueness, mixing, boundary layer, blowups, and stochasticity through interdisciplinary approaches. For example, the technique of convex integration, originating in geometry, led to results on nonuniqueness of solutions to PDEs of fluid mechanics and recently even singular stochastic PDEs driven by noise, for which the existence of solutions had long been open.

 The objective of this research project “Recent Developments in Fluid Mechanics PDEs” is to gather a large group of active, influential, and internationally renowned researchers in fluid mechanics PDEs and organize three workshops in May-June 2027 at RIMS, in collaboration with the annual winter workshop on fluid mechanics held at Kyoto University. Our workshops will allow ample time for interactions, enabling in-depth discussions that can lead to future collaborations. We may open our workshops to the public so that young scholars in Japan can get exposed to such cutting-edge research through inspiring lectures.