具跳跃型乘性噪声的随机流体动力学系统的强解
概率论
2014-07-23 v3
摘要
本文证明了在 () 的无界和有界区域上，若干随机流体动力学系统存在唯一的最大强解（在偏微分方程意义下）。对于二维随机流体动力学系统，该最大解被证明是全局解。我们的框架具有通用性，能够求解具跳跃型扰动的 Navier-Stokes 方程、MHD 方程、磁性 B\'enard 问题、B\'enard 对流的 Boussinesq 模型、湍流壳层模型以及 Leray- 模型。我们通过证明关于具局部 Lipschitz 连续系数的抽象随机偏微分方程的最大解和全局解存在性的一般结果来实现这一目标。证明方法基于某些截断和不动点方法。
引用
@article{arxiv.1402.5772,
title = {Strong solutions to stochastic hydrodynamical systems with multiplicative noise of jump type},
author = {Hakima Bessaih and Erika Hausenblas and Paul Razafimandimby},
journal= {arXiv preprint arXiv:1402.5772},
year = {2014}
}
备注
Submitted for publication. Minor correction (typos) have been made. This paper is about strong (more regular in space!) solution of some hydrodynamic equations driven by Levy noise. We use abstract framework as in arXiv:0807.1810 and the examples we took are borrowed from arXiv:0807.1810 which is acknowledged in our text