Geodesic
A short note on $L^q$ theory for Stokes problem with a pressure-dependent viscosity
Czechoslovak Mathematical Journal, Tome 66 (2016) no. 2, pp. 317-329.

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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 $T(Du,p):=\nu (p,|D|^2)D$ 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).
DOI : 10.1007/s10587-016-0258-x
Classification : 35B65, 35Q35, 76D03
Keywords: Stokes problem; $L^q$ theory; pressure-dependent viscosity 
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     title = {A short note on $L^q$ theory for {Stokes} problem with a pressure-dependent viscosity},
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Mácha, Václav. A short note on $L^q$ theory for Stokes problem with a pressure-dependent viscosity. Czechoslovak Mathematical Journal, Tome 66 (2016) no. 2, pp. 317-329. doi : 10.1007/s10587-016-0258-x. http://geodesic.mathdoc.fr/articles/10.1007/s10587-016-0258-x/

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