Navier-Stokes 方程的平稳与间断弱解
偏微分方程分析
2020-08-24 v5
摘要
我们证明三维 Navier-Stokes 方程（NSE）存在非平凡有限能量周期平稳弱解。该构造依赖于一种凸积分格式，利用专为 NSE 设计的新型平稳构造块。所构造的近似平稳解族也被用于证明 NSE 具有在具有正 Lebesgue 测度的稠密集上能量剖面间断的弱解的存在性。
关键词
引用
@article{arxiv.1901.07485,
title = {Stationary and discontinuous weak solutions of the Navier-Stokes equations},
author = {Alexey Cheskidov and Xiaoyutao Luo},
journal= {arXiv preprint arXiv:1901.07485},
year = {2020}
}
备注
Unfortunately, a critical error was found in the construction in Section 3 and the weak solutions constructed based on the building blocks in Section 3 were not divergence-free