On the uniqueness for weak solutions of steady double-phase fluids-Reference-Cited by-同舟云学术

On the uniqueness for weak solutions of steady double-phase fluids

Published:2021-09-08 Issue:1 Volume:11 Page:454-468
ISSN:2191-950X
Container-title:Advances in Nonlinear Analysis
language:en
Short-container-title:

Author:

Abdelwahed Mohamed¹,Berselli Luigi C.²,Chorfi Nejmeddine¹

Affiliation:

1. Department of Mathematics, College of Sciences, King Saud University , , Riyadh 11451 , Saudi Arabia

2. Dipartimento di Matematica Università di Pisa Via F. Buonarroti 1/c , Pisa I-56127 , Italy

Abstract

Abstract We consider a double-phase non-Newtonian fluid, described by a stress tensor which is the sum of a p-Stokes and a q-Stokes stress tensor, with 1 < p<2 < q<∞. For a wide range of parameters (p, q), we prove the uniqueness of small solutions. We use the p < 2 features to obtain quadratic-type estimates for the stress-tensor, while we use the improved regularity coming from the term with q > 2 to justify calculations for weak solutions. Results are obtained through a careful use of the symmetries of the convective term and are also valid for rather general (even anisotropic) stress-tensors.

Publisher

Walter de Gruyter GmbH

Subject

Analysis

Link

https://www.degruyter.com/document/doi/10.1515/anona-2020-0196/pdf

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