On a Burgers type nonlinear equation perturbed by a pure jump Lévy noise in Rd

Abstract

In this paper, we study a stochastic fractional Burgers type nonlinear equation driven by a pure jump Lévy space–time white noise with d-dimensional spatial variables x∈Rd. Our equation involves a Markovian generator of a stable-like Feller process with variable order α(x). Under certain polynomial growth conditions, we establish the existence and uniqueness of an Lp(Rd)-valued (local) solution for the initial value problem to our equation. Our approaches are essentially based on the estimates of the fundamental solution to the stable-like Markovian generator and the Lp-theory of the stochastic integral with respect to the pure jump Lévy space–time white noise.