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Uniqueness and regularity of flows of non-Newtonian fluids with critical power-law growth Kaplicky, Petr
Description
We deal with the flows of non-Newtonian fluids in three dimensional setting subjected to the homogeneous Dirichlet boundary condition. Under the natural monotonicity, coercivity and growth condition on the Cauchy stress tensor expressed by a critical power index $p=\frac{11}{5}$ we show that a Gehring type argument is applicable which allows to improve regularity of any weak solution. Improving further the regularity of weak solutions along a regularity ladder allows to show that actually solution belongs to a uniqueness class provided data of the problem are sufficiently smooth.
We also briefly discuss if the similar technique is applicable to critical Convective Brinkman-Forchheimer equation.
Item Metadata
| Title |
Uniqueness and regularity of flows of non-Newtonian fluids with critical power-law growth
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| Creator | |
| Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
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| Date Issued |
2020-11-26T08:54
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| Description |
We deal with the flows of non-Newtonian fluids in three dimensional setting subjected to the homogeneous Dirichlet boundary condition. Under the natural monotonicity, coercivity and growth condition on the Cauchy stress tensor expressed by a critical power index $p=\frac{11}{5}$ we show that a Gehring type argument is applicable which allows to improve regularity of any weak solution. Improving further the regularity of weak solutions along a regularity ladder allows to show that actually solution belongs to a uniqueness class provided data of the problem are sufficiently smooth. We also briefly discuss if the similar technique is applicable to critical Convective Brinkman-Forchheimer equation. |
| Extent |
20.0 minutes
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| Subject | |
| Type | |
| File Format |
video/mp4
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| Language |
eng
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| Notes |
Author affiliation: Charles University
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| Series | |
| Date Available |
2021-05-26
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| Provider |
Vancouver : University of British Columbia Library
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| Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
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| DOI |
10.14288/1.0398153
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| URI | |
| Affiliation | |
| Peer Review Status |
Unreviewed
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| Scholarly Level |
Researcher
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| Rights URI | |
| Aggregated Source Repository |
DSpace
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Rights
Attribution-NonCommercial-NoDerivatives 4.0 International