A high regularity result of solutions to modified p-Stokes equations

2013/08/05 by Francesca Crispo, Paolo Maremonti, Crispo, Francesca +1
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Elasticity and Material Modeling #FOS: Mathematics #Navier-Stokes equation solutions #math.AP

paper · pdf · doi:10.48550/arxiv.1308.0980

arxiv created 2013/08/05 · openalex publication_date 2013/08/05 · arxiv updated 2013/08/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper is concerned with a special elliptic system, which can be seen as a perturbed p-Laplacean system, p∈(1,2), and, for its "shape", it is close to the p-Stokes system. Since our "stress tensor" is given by means of ∇ u and not by its symmetric part, then our system is not a p-Stokes system. Hence, the system is called \it modified p-Stokes system. We look for the high regularity of the solutions (u,π), that is D²u,∇π∈ L^q,q∈(1,∞). In particular, we get ∇ u,π∈ C^0,α. As far as we know, such a result of high regularity is the first concerning the coupling of unknowns (u,π). However, our result also holds for the p-Laplacean, and it is the first high regularity result in unbounded domains.

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