Mathematica Bohemica, first online, pp. 1-19


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

Cholmin Sin, Sin-Il Ri

Received December 22, 2020.   Published online February 7, 2022.

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.
Keywords:  existence of weak solutions; electrorheological fluid; Lipschitz truncation; variable exponent
Classification MSC:  35D30, 35A23, 46E30, 46E35, 76D03, 76A05
DOI:  10.21136/MB.2022.0200-20

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Affiliations:   Cholmin Sin, Sin-Il Ri, Institute of Mathematics, State Academy of Sciences, KwaHaK-1Dong, Unjong District, Pyongyang, Democratic People's Republic of Korea, e-mail: sincm1223@star-co.net.kp, si.ri@star-co.net.kp


 
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