Geodesic
Existence of weak solutions for steady flows of electrorheological fluid with Navier-slip type boundary conditions
Mathematica Bohemica, Tome 147 (2022) no. 4, pp. 567-585

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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 $p(x)>2n/(n+2)$. 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.
DOI : 10.21136/MB.2022.0200-20
Classification : 35A23, 35D30, 46E30, 46E35, 76A05, 76D03
Keywords: existence of weak solutions; electrorheological fluid; Lipschitz truncation; variable exponent 
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Sin, Cholmin; Ri, Sin-Il. Existence of weak solutions for steady flows of electrorheological fluid with Navier-slip type boundary conditions. Mathematica Bohemica, Tome 147 (2022) no. 4, pp. 567-585. doi: 10.21136/MB.2022.0200-20

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