Ujjwal Koley


TIFR CAM Bangalore

Page web: https://www.math.tifrbng.res.in/people/ujjwal 

Title: Convex integration solutions for stochastic transport equation

Abstract: In this talk, we shall consider a transport equation forced by a random noise of three types: additive, linear multiplicative, transport in Stratonovich’s interpretation. Via convex integration modified to probabilistic setting, we will show existence of a divergence-free vector field with spatial regularity in Sobolev space and corresponding solution to a transport equation with spatial regularity in Lebesgue space, and consequently non-uniqueness in law at the level of probabilistically strong solutions globally in time.