Exit Times of Diffusions with Incompressible Drift

Let Rn be a bounded domain and for x let (x) be the expected exit time from of a diffusing particle starting at x and advected by an incompressible flow u. We are interested in the question which flows maximize L(), that is, they are most efficient in the creation of hotspots inside . Surprisingly, among all simply connected domains in two dimensions, the discs are the only ones for which the zero flow u 0 maximises L(). We also show that in any dimension, among all domains with a fixed volume and all incompressible flows on them, L() is maximized by the zero flow on the ball.

• Type: Journal
• Year: 2010
• Where: SIAMMA
• Authors: Gautam Iyer, Alexei Novikov, Lenya Ryzhik, Andrej Zlatos
• Keywords: Exit Time, Incompressible Flows, SIAMMA 2010, Simply Connected