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Solvability of the Stochastic Degasperis-Procesi Equation
Journal of Dynamics and Differential Equations ( IF 1.4 ) Pub Date : 2021-06-16 , DOI: 10.1007/s10884-021-10021-5 Lynnyngs K. Arruda , Nikolai V. Chemetov , Fernanda Cipriano
中文翻译:
随机 Degasperis-Procesi 方程的可解性
更新日期:2021-06-17
Journal of Dynamics and Differential Equations ( IF 1.4 ) Pub Date : 2021-06-16 , DOI: 10.1007/s10884-021-10021-5 Lynnyngs K. Arruda , Nikolai V. Chemetov , Fernanda Cipriano
This article studies the Stochastic Degasperis-Procesi 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.
中文翻译:
随机 Degasperis-Procesi 方程的可解性
本文研究了带有加性噪声的\( \mathbb {R}\)上的 Stochastic Degasperis-Procesi 方程。应用动力学理论,并考虑\(L^2(\mathbb {R})\cap L^{2+\delta }( \mathbb {R})\) 中的初始条件,对于任意小的\(\delta >0\),我们建立了全局路径解的存在。限于零噪声的特殊情况,我们的结果改进了文献中存在的确定性可解性结果。