In this paper, we study the stochastic Navier–Stokes equations (SNSE) perturbed by Lévy noise in three dimensions with a hereditary viscous term which depends on the past history. We establish the local solvability of the Cauchy problem for such systems. The local monotonicity property of the nonlinear term of the cutoff problem and a stochastic generalization of the Minty–Browder technique are exploited in the proofs. Finally, we show that the global solvability results hold under smallness condition on the initial data and suitable assumptions on the noise coefficients.

中文翻译：

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具有遗传粘度的 Lévy 噪声扰动的随机 Navier-Stokes 方程

在本文中，我们研究了由 Lévy 噪声在三个维度上扰动的随机 Navier-Stokes 方程（SNSE），该方程具有依赖于过去历史的遗传粘性项。我们为此类系统建立了柯西问题的局部可解性。证明中利用了截止问题的非线性项的局部单调性和 Minty-Browder 技术的随机推广。最后，我们证明了全局可解性结果在初始数据较小的条件下和对噪声系数的适当假设下成立。