Existence of weak solutions for steady flows of electrorheological fluid with Navier-slip type boundary conditions
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...
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| Format: | Article |
| Language: | English |
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Institute of Mathematics of the Czech Academy of Science
2022-12-01
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| Series: | Mathematica Bohemica |
| Subjects: | |
| Online Access: | http://mb.math.cas.cz/full/147/4/mb147_4_9.pdf |
| _version_ | 1828098917069225984 |
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| author | Cholmin Sin Sin-Il Ri |
| author_facet | Cholmin Sin Sin-Il Ri |
| author_sort | Cholmin Sin |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-11T08:09:25Z |
| format | Article |
| id | doaj.art-a3b85d0359f1493aaa3abe94a47d0b02 |
| institution | Directory Open Access Journal |
| issn | 0862-7959 2464-7136 |
| language | English |
| last_indexed | 2024-04-11T08:09:25Z |
| publishDate | 2022-12-01 |
| publisher | Institute of Mathematics of the Czech Academy of Science |
| record_format | Article |
| series | Mathematica Bohemica |
| spelling | doaj.art-a3b85d0359f1493aaa3abe94a47d0b022022-12-22T04:35:26ZengInstitute of Mathematics of the Czech Academy of ScienceMathematica Bohemica0862-79592464-71362022-12-01147456758510.21136/MB.2022.0200-20MB.2022.0200-20Existence of weak solutions for steady flows of electrorheological fluid with Navier-slip type boundary conditionsCholmin SinSin-Il RiWe 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.http://mb.math.cas.cz/full/147/4/mb147_4_9.pdf existence of weak solutions electrorheological fluid lipschitz truncation variable exponent |
| spellingShingle | Cholmin Sin Sin-Il Ri Existence of weak solutions for steady flows of electrorheological fluid with Navier-slip type boundary conditions Mathematica Bohemica existence of weak solutions electrorheological fluid lipschitz truncation variable exponent |
| title | Existence of weak solutions for steady flows of electrorheological fluid with Navier-slip type boundary conditions |
| title_full | Existence of weak solutions for steady flows of electrorheological fluid with Navier-slip type boundary conditions |
| title_fullStr | Existence of weak solutions for steady flows of electrorheological fluid with Navier-slip type boundary conditions |
| title_full_unstemmed | Existence of weak solutions for steady flows of electrorheological fluid with Navier-slip type boundary conditions |
| title_short | Existence of weak solutions for steady flows of electrorheological fluid with Navier-slip type boundary conditions |
| title_sort | existence of weak solutions for steady flows of electrorheological fluid with navier slip type boundary conditions |
| topic | existence of weak solutions electrorheological fluid lipschitz truncation variable exponent |
| url | http://mb.math.cas.cz/full/147/4/mb147_4_9.pdf |
| work_keys_str_mv | AT cholminsin existenceofweaksolutionsforsteadyflowsofelectrorheologicalfluidwithnaviersliptypeboundaryconditions AT sinilri existenceofweaksolutionsforsteadyflowsofelectrorheologicalfluidwithnaviersliptypeboundaryconditions |