线性阻尼KdV方程在跳跃噪声驱动下的well-posed性与不变测度的存在性
Well-posedness and existence of an invariant measure for the linearly-damped KdV equations driven by a jump noise
AI总结：
本文研究了线性阻尼KdV方程在跳跃噪声下的well-posed性及不变测度存在性，证明了在足够大的阻尼系数下系统存在不变测度。
摘要：
本文研究了在单位圆环$\mathbb{T}$上受乘性莱维噪声扰动的线性阻尼KdV方程。对于任何阻尼系数$γ> 0$，我们建立了值域在$H^2(\mathbb{T})$上的路径弱解的存在性和唯一性。在论文的第二部分，我们分析了这些解的长期行为。这项研究尤为微妙，因为时间中的跳跃可能显著影响渐进行为。我们利用Maslowski和Seidler的技术证明，只要摩擦阻尼系数$γ> 0$足够大，受平方可积跳跃影响的系统在$H^2(\mathbb{T})$中存在不变测度。
英文摘要：
In this paper, we investigate the linearly damped KdV equation on the one-dimensional torus $\mathbb{T}$, perturbed by a multiplicative Lévy noise. For any damping coefficient $γ> 0$, we establish the existence and uniqueness of a pathwise weak solution with values in $H^2(\mathbb{T})$. In the second part of the paper, we analyze the long-time behavior of these solutions. This study is particularly subtle as the presence of jumps in time can significantly influence the asymptotics. We show, using the techniques of Maslowski and Seidler, that, provided the frictional damping coefficient $γ> 0$ is sufficiently large, the system influenced by square-integrable jumps admits an invariant measure in $H^2(\mathbb{T})$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
