Article
MSC:
35A23,
35D30,
46E30,
46E35,
76A05,
76D03 | MR 4512174 | Zbl 07655827 | DOI: 10.21136/MB.2022.0200-20
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Keywords:
existence of weak solutions; electrorheological fluid; Lipschitz truncation; variable exponent
existence of weak solutions; electrorheological fluid; Lipschitz truncation; variable exponent
Summary:
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.
References:
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