论文标题
三维随机趋化性趋化 - 纳维尔 - 塞托克斯系统的全球martingale弱解决方案与莱维工艺
Global martingale weak solutions for the three-dimensional stochastic chemotaxis-Navier-Stokes system with Lévy processes
论文作者
论文摘要
本文研究了在有界结构域中遭受lévy型随机外力的三维随机趋化性 - 纳维尔 - 塞托克斯（SCNS）系统。到目前为止，关于SCNS系统的全球可溶性的现有结果主要集中在两个空间维度的情况下，SCNS系统在第三维中鲜为人知。我们在目前的工作中证明，在适当的假设下，三维SCNS系统至少具有一个全球的Martingale解决方案，这在分析意义和随机意义上都是弱的。得出了一种新的熵能量不平等和统一界限估计的随机类似物，这使我们能够通过收缩映射原理从适当正则化的SCNS系统中构建全球及时的近似解决方案。 Martingale解决方案存在的证明是基于随机紧凑度方法和对限制程序的精心识别，其中Jakubowski-Skorokhod定理用于处理配备有弱拓扑的相位空间。
This paper studies the three-dimensional stochastic chemotaxis-Navier-Stokes (SCNS) system subjected to a Lévy-type random external force in bounded domain. Up to now, the existing results concerning global solvability of SCNS system mainly concentrated on the case of two spacial dimensions, little is known for the SCNS system in dimension three. We prove in present work that the three-dimensional SCNS system possesses at least one global martingale solution under proper assumptions, which is weak both in the analytical sense and in the stochastic sense. A new stochastic analogue of entropy-energy inequality and an uniform boundedness estimate are derived, which enable us to construct global-in-time approximate solutions from a properly regularized SCNS system via the Contraction Mapping Principle. The proof of the existence of martingale solution is based on the stochastic compactness method and an elaborate identification of the limits procedure, where the Jakubowski-Skorokhod Theorem is applied to deal with the phase spaces equipped with weak topology.
