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arXiv · 2302.09223

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

Yuanyuan Feng·Lei Li·Jian-Guo Liu·Xiaoqian Xu
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Abstract

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 $W_0^{1,p}(\Omega)$ 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.

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Yuanyuan Feng, Lei Li, Jian-Guo Liu, Xiaoqian Xu. 2023-02-18. Existence of weak solutions to $p$-Navier-Stokes equations. https://arxiv.org/abs/2302.09223

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