Existence of weak solutions for steady flows of electrorheological fluid with Navier-slip type boundary conditions

Cholmin Sin; Sin-Il Ri

Mathematica Bohemica (2022)

  • Volume: 147, Issue: 4, page 567-585
  • ISSN: 0862-7959

Abstract

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We prove the existence of weak solutions for steady flows of electrorheological fluids with homogeneous Navier-slip type boundary conditions provided p ( x ) > 2 n / ( n + 2 ) . To prove this, we show Poincaré- and Korn-type inequalities, and then construct Lipschitz truncation functions preserving the zero normal component in variable exponent Sobolev spaces.

How to cite

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Sin, Cholmin, and Ri, Sin-Il. "Existence of weak solutions for steady flows of electrorheological fluid with Navier-slip type boundary conditions." Mathematica Bohemica 147.4 (2022): 567-585. <http://eudml.org/doc/298785>.

@article{Sin2022,
abstract = {We prove the existence of weak solutions for steady flows of electrorheological fluids with homogeneous Navier-slip type boundary conditions provided $p(x)>2n/(n+2)$. To prove this, we show Poincaré- and Korn-type inequalities, and then construct Lipschitz truncation functions preserving the zero normal component in variable exponent Sobolev spaces.},
author = {Sin, Cholmin, Ri, Sin-Il},
journal = {Mathematica Bohemica},
keywords = {existence of weak solutions; electrorheological fluid; Lipschitz truncation; variable exponent},
language = {eng},
number = {4},
pages = {567-585},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Existence of weak solutions for steady flows of electrorheological fluid with Navier-slip type boundary conditions},
url = {http://eudml.org/doc/298785},
volume = {147},
year = {2022},
}

TY - JOUR
AU - Sin, Cholmin
AU - Ri, Sin-Il
TI - Existence of weak solutions for steady flows of electrorheological fluid with Navier-slip type boundary conditions
JO - Mathematica Bohemica
PY - 2022
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 147
IS - 4
SP - 567
EP - 585
AB - We prove the existence of weak solutions for steady flows of electrorheological fluids with homogeneous Navier-slip type boundary conditions provided $p(x)>2n/(n+2)$. To prove this, we show Poincaré- and Korn-type inequalities, and then construct Lipschitz truncation functions preserving the zero normal component in variable exponent Sobolev spaces.
LA - eng
KW - existence of weak solutions; electrorheological fluid; Lipschitz truncation; variable exponent
UR - http://eudml.org/doc/298785
ER -

References

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