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

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Abstract

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 ∈ (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).

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Authors and Affiliations

  1. Institute of Mathematics, Czech Academy of Sciences, Žitná 25, 115 67, Praha 1, Czech Republic

    Václav Mácha

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  1. Václav Mácha
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Correspondence to Václav Mácha.

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This work was supported by the GA ČR project GA13-00522S in the general framework of RVO: 67985840.

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Mácha, V. A short note on L q theory for Stokes problem with a pressure-dependent viscosity. Czech Math J 66, 317–329 (2016). https://doi.org/10.1007/s10587-016-0258-x

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