Well-posedness of the Stochastic Degasperis-Procesi Equation
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 $L^2(\mathbb{R})\cap L^{2+δ}(\mathbb{R})$, for arbitrary small $δ>0$, 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.
math.PR↗