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

Václav Mácha

Czechoslovak Mathematical Journal (2016)

  • Volume: 66, Issue: 2, page 317-329
  • ISSN: 0011-4642

Abstract

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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 ( D u , p ) : = ν ( 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).

How to cite

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Mácha, Václav. "A short note on $L^q$ theory for Stokes problem with a pressure-dependent viscosity." Czechoslovak Mathematical Journal 66.2 (2016): 317-329. <http://eudml.org/doc/280107>.

@article{Mácha2016,
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 $T(Du,p):=\nu (p,|D|^2)D$ 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).},
author = {Mácha, Václav},
journal = {Czechoslovak Mathematical Journal},
keywords = {Stokes problem; $L^q$ theory; pressure-dependent viscosity},
language = {eng},
number = {2},
pages = {317-329},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A short note on $L^q$ theory for Stokes problem with a pressure-dependent viscosity},
url = {http://eudml.org/doc/280107},
volume = {66},
year = {2016},
}

TY - JOUR
AU - Mácha, Václav
TI - A short note on $L^q$ theory for Stokes problem with a pressure-dependent viscosity
JO - Czechoslovak Mathematical Journal
PY - 2016
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 66
IS - 2
SP - 317
EP - 329
AB - 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).
LA - eng
KW - Stokes problem; $L^q$ theory; pressure-dependent viscosity
UR - http://eudml.org/doc/280107
ER -

References

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