Well-posedness of the Stochastic Degasperis-Procesi Equation

Abstract

This article studies the Stochastic Degasperis-Procesi (SDP) equation on $\mathbb{R}$ with an additive noise. Applying the kinetic theory, and considering the initial conditions in $L^2(\mathbb{R})\cap L^{2+\delta }(\mathbb{R})$, for arbitrary small $\delta >0$, we establish the existence of a global pathwise solution. Restricting to the particular case of zero noise, our result improves the deterministic solvability results that exist in the literature.

References in corpus (1)

• Degasperis-Procesi peakons and the discrete cubic string

Cited by in corpus (1)

• Weak solution for Stochastic Degasperis-Procesi Equation