Quasilinear rough partial differential equations with transport noise

Antoine Hocquet

Published 2018-08-29Version 1

We investigate the Cauchy problem for a quasilinear equation of the form $\mathrm d u=\mathrm{div}(A(t,x,u)\nabla u)\mathrm d t +\sigma (t,x)\nabla u\mathrm d X,$ $u_0\in L^2$ on the torus $\mathbb T^d$, where $X$ is a two-step geometric rough path. Using an energy approach, we provide sufficient conditions guaranteeing existence and uniqueness.