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arXiv 2302.09223math.AP
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$p$ -Navier-斯托克斯方程弱解的存在性

Existence of weak solutions to $p$-Navier-Stokes equations

Yuanyuan Feng, Lei Li, Jian-Guo Liu, Xiaoqian Xu

摘要:

研究了有界区域上具有对称$p$ -Laplacian算子的$p$ -Navier-斯托克斯方程弱解的存在性.在$W_0^{1,p}(Ω)$中构造了一个特殊的Schauder基,并利用Galerkin逼近证明了该Schauder基的弱解的存在性.同时,在证明中,我们建立了弱解的$L^p$范数的链式法则,弥补了我们以前工作中的不足。对于所考虑的弱解,也建立了能量耗散的等价性。

英文摘要:

We study the existence of weak solutions to the $p$-Navier-Stokes equations with a symmetric $p$-Laplacian on bounded domains. We construct a particular Schauder basis in $W_0^{1,p}(Ω)$ with divergence free constraint and prove existence of weak solutions using the Galerkin approximation via this basis. Meanwhile, in the proof, we establish a chain rule for the $L^p$ norm of the weak solutions, which fixes a gap in our previous work. The equality of energy dissipation is also established for the weak solutions considered.

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。

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