发表机构
Huazhong University of Science and Technology（华中科技大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对带保守 Marcus 噪声的三维聚焦能量临界薛定谔方程，建立了全局适定性与几乎必然散射，通过结合能量临界稳定性与 Poisson Strichartz 估计实现。
AI 中文摘要
本文建立了三维聚焦能量临界非线性薛定谔方程在保守线性 Marcus 噪声下的全局适定性。对于任意确定性能量空间初值，我们构造了一个概率意义上的强解，该解在临界时空类中是唯一的，并证明了有限活动近似的收敛性。空间轮廓只需有界且 Lipschitz 连续，而中心化的纯跳 Lévy 噪声假定具有有限二阶矩。若时间噪声系数在半直线上平方可积，则解几乎必然散射，具有均匀均方尾部收敛且无小性限制。该解守恒质量并满足精确的能量平衡。证明结合了确定性能量临界稳定性与 Poisson Strichartz 估计；相互作用表示鞅的收敛性给出了继续延拓和散射所需的临界时空控制。
英文摘要
This work establishes global well-posedness for the three-dimensional defocusing energy-critical nonlinear Schrödinger equation with conservative linear Marcus noise. For arbitrary deterministic energy-space data, we construct a probabilistically strong solution, unique in the critical spacetime class, and prove convergence of finite-activity approximations. The spatial profiles need only be bounded and Lipschitz, while the centered pure-jump Lévy noise is assumed to have finite second moment. If the temporal noise coefficient is square integrable on the half-line, the solution scatters almost surely, with uniform mean-square tail convergence and no smallness restriction. The solution conserves mass and satisfies an exact energy balance. The proof combines deterministic energy-critical stability with Poisson Strichartz estimates; convergence of the interaction-representation martingale gives the critical spacetime control needed for continuation and scattering.
