Quelques problèmes de la théorie des rough paths : méthodes de cubature et équations aux dérivés partielles

Taking the path less travelled: rough paths and perturbations

Khalil Chouk is deliberately going through a rough patch. “The application of rough paths to partial differential equations (PDEs) is still not well developed,” he explains. “Building on research in stochastic PDEs and the theory of rough paths, I am proposing an original approach to understanding the behaviour of the Korteweg-de Vries equation—a mathematical model of waves on shallow water surfaces—in the presence of noise.” The goal is to answer questions ranging from the basic (the existence and uniqueness of solutions) to the more complex (such as effective numerical schemes and long-time behaviour). “This study offers promising perspectives in a variety of exciting areas such as environmental models. For example, it can be used to develop a more realistic model for climate change-related risks such as flooding,” Chouk says.