Local energy weak solutions for the Navier-Stokes equations in the half-space
Local energy weak solutions for the Navier-Stokes equations in the half-space
复制标题
半空间纳维-斯托克斯方程的局域能量弱解
DOI：
10.1007/s00220-019-03344-4
复制
发表时间：
2019
期刊：
影响因子：
--
通讯作者：
C.
中科院分区：
文献类型：
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作者：
Maekawa;Y.;Miura;H.;and Prange;C.
本文的目的是证明半空间中纳维-斯托克斯方程全局及时局部能量弱解的存在性。在整个空间中，此类解决方案有时被称为 Lemarié-Rieusset 解决方案。我们工作中的主要工具是压力的显式表示公式，由于边界的原因，该公式被分解为亥姆霍兹-勒雷部分和谐波部分。我们还解释了我们的结果如何能够反驳 Barker 和 Seregin 在有限时间内开发奇点的解决方案所获得的尺度临界范数的爆炸。
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. Such solutions are sometimes called Lemarié–Rieusset solutions in the whole space. 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-criticalnorm obtained by Barker and Seregin for solutions developing a singularity in finite time.