A short note on $L^q$ theory for Stokes problem with a pressure-dependent viscosity

0460394 - MÚ 2017 RIV CZ eng J - Journal Article
Mácha, Václav
A short note on $L^q$ theory for Stokes problem with a pressure-dependent viscosity.
Czechoslovak Mathematical Journal. Roč. 66, č. 2 (2016), s. 317-329. ISSN 0011-4642. E-ISSN 1572-9141
R&D Projects: GA ČR GA13-00522S
Institutional support: RVO:67985840
Keywords : Stokes problem * Lq theory * pressure-dependent viscosity
Subject RIV: BA - General Mathematics
Impact factor: 0.364, year: 2016
http://hdl.handle.net/10338.dmlcz/145726

We study higher local integrability of a weak solution to the steady Stokes problem. We consider the case of a pressure- and shear-rate-dependent viscosity, i.e., the elliptic part of the Stokes problem is assumed to be nonlinear and it depends on p and on the symmetric part of a gradient of u, namely, it is represented by a stress tensor T (Du, p):= v(p, |D|2)D which satisfies r-growth condition with r in (1, 2]. In order to get the main result, we use Calderón-Zygmund theory and the method which was presented for example in the paper Caffarelli, Peral (1998).
Permanent Link: http://hdl.handle.net/11104/0260495