Existence of martingale solutions to a stochastic kinetic model of chemotaxis

Abstract

We show the existence of local and global in time weak martingale solutions for a stochastic version of the Othmer-Dunbar-Alt kinetic model of chemotaxis under suitable assumptions on the turning kernel and stochastic drift coefficients, using dispersion and stochastic Strichartz estimates. The analysis is based on new Strichartz estimates for stochastic kinetic transport. The derivation of these estimates involves a local in time dispersion analysis using properties of stochastic flows, and a time-splitting argument to extend the local in time results to arbitrary time intervals.