Existence of weak solutions to p-Navier-Stokes equations

2023/02/18 by Yuanyuan Feng, Feng, Yuanyuan, Lei Li +5
Engineering · Mathematics · #35Q30 #35Q35 #76D03 #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Nonlinear Partial Differential Equations #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2302.09223

openalex publication_date 2023/02/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 W₀^1,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.

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