Global Calderón--Zygmund theory for parabolic p-Laplacian system: the case 1

2021/09/06 by Ke Chen, Chen, Ke, Quoc‐Hung Nguyen +3
Mathematics · #Advanced Mathematical Physics Problems #Nonlinear Partial Differential Equations #Navier-Stokes equation solutions

paper · doi:10.48550/arxiv.2109.02595

Abstract

The aim of this paper is to establish global Calderón--Zygmund theory to parabolic p-Laplacian system: u_t -div(|∇ u|^p-2∇ u) = div (|F|^p-2F)~in~Ω× (0,T)⊂ ℝⁿ⁺¹, proving that F∈ L^q⇒ ∇ u∈ L^q, for any q>max\p,(n(2-p))/(2)\ and p>1. Acerbi and Mingione \citeAcerbi07 proved this estimate in the case p>(2n)/(n+2). In this article we settle the case 1

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