各向异性可压缩 Stokes 系统弱解的全局存在性
偏微分方程分析
2022-03-24 v3
摘要
本文研究具有各向异性黏性张量的准静态可压缩 Stokes 方程的弱解全局存在性问题。我们证明的关键要素是对与压力相关的特定缺陷测度的控制，这避免了有效通量的使用。利用这一新工具，我们解决了一个公开问题，即对此类系统在不对各项异性幅度施加任何限制的条件下给出 à la Leray 意义的全局解存在性。这为处理可压缩拟线性 Stokes 系统提供了一种灵活而自然的途径，此类系统在生物学、多孔介质、超导或低雷诺数 regime 下的其他应用中十分重要。
引用
@article{arxiv.1907.09171,
title = {Global Existence of Weak Solutions for the Anisotropic Compressible Stokes System},
author = {Didier Bresch and Cosmin Burtea},
journal= {arXiv preprint arXiv:1907.09171},
year = {2022}
}
备注
Compared to the version in Ann. IHP. : Revised argument in the proof of Theorem 2.10, main results unchanged : the proof of the main result was incomplete because we cannot prove that the defect measure vanishes at initial time. We prove instead that the mean value of the defect measure over any interval [0,T] is 0. This is sufficient in order to identify the pressure. See Lemmas 2.11 and 2.12