Special Session 19: Stochastic Partial Differential Equations

Convex integration techniques in stochastic fluid dynamics

Andre Schenke
Courant Institute of Mathematical Sciences
Convex integration is a technique that was pioneered by John Nash almost 70 years ago in his study of the isometric embedding problem. More recently, in about the last 15 years, the technique has seen spectacular success when applied by Buckmaster, De Lellis, Isett, Sz\`{e}kelyhidi, Vicol and others to various equations of fluid dynamics (in particular Euler and Navier--Stokes equations). More recently, in the last 5 years, it has been applied by an increasing number of people (following pioneering works of Hofmanov\`{a}, Zhu and Zhu) to the equations of stochastic fluid dynamics. In this talk I will report recent convex integration results for stochastic fluid dynamical equations yielding nonuniqueness in law for those equations.