arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 1711.04486math.AP
收藏

半空间中Navier-斯托克斯方程的局部能量弱解

Local energy weak solutions for the Navier-Stokes equations in the half-space

Yasunori Maekawa, Hideyuki Miura, Christophe Prange

摘要:

证明了半空间$\mathbb R^3_+$中Navier-斯托克斯方程整体及时局部能量弱解的存在性.这样的解有时称为全空间$\mathbb R^3$中的Lemarié-Rieusset解。在我们的工作中的主要工具是一个显式的表示公式的压力,这是分解成一个Helmholtz-Leray部分和调和部分,由于边界。我们还解释了我们的结果如何能够reprove爆破的规模临界$L^3(\mathbb R^3_+)$规范巴克和Seregin的解决方案开发的奇异性在有限时间内获得。

英文摘要:

The purpose of this paper is to prove the existence of global in time local energy weak solutions to the Navier-Stokes equations in the half-space $\mathbb R^3_+$. Such solutions are sometimes called Lemarié-Rieusset solutions in the whole space $\mathbb R^3$. The main tool in our work is an explicit representation formula for the pressure, which is decomposed into a Helmholtz-Leray part and a harmonic part due to the boundary. We also explain how our result enables to reprove the blow-up of the scale-critical $L^3(\mathbb R^3_+)$ norm obtained by Barker and Seregin for solutions developing a singularity in finite time.

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。

↑