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Well-posedness of the Stochastic Degasperis-Procesi Equation
Lynnyngs K. Arruda, Nikolai V. Chemetov, Fernanda Cipriano · 2024-09-01 · via math.PR updates on arXiv.org

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.

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