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Regularity of Navier--Stokes flows with bounds for the pressure Tran, Chuong Van
Description
This talk is concerned with global regularity of solutions of the Navier--Stokes equations. Let $\Omega(t) \assign \{x:|u(x,t)| > c\norm{u}_{L^r}\}$, for some $r\ge3$ and constant $c$ independent of $t$, with measure $|\Omega|$. It is shown that if $\int_\Omega|p+\mathcal{P}|^{3/2}\mathd x$ becomes sufficiently small as $|\Omega|$ decreases, then $\norm{u}_{L^{(r+6)/3}}$ decays and regularity is secured. Here $p$ is the physical pressure and $\mathcal{P}$ is a pressure moderator of relatively broad forms. The implications of the results are discussed and regularity criteria in terms of bounds for $|p+\mathcal{P}|$ within $\Omega$ are deduced. This is joint work with Xinwei Yu.
Item Metadata
Title |
Regularity of Navier--Stokes flows with bounds for the pressure
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Creator | |
Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
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Date Issued |
2016-06-07T14:20
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Description |
This talk is concerned with global regularity of solutions of the Navier--Stokes
equations. Let $\Omega(t) \assign \{x:|u(x,t)| > c\norm{u}_{L^r}\}$, for some
$r\ge3$ and constant $c$ independent of $t$, with measure $|\Omega|$.
It is shown that if $\int_\Omega|p+\mathcal{P}|^{3/2}\mathd x$ becomes
sufficiently small as $|\Omega|$ decreases, then $\norm{u}_{L^{(r+6)/3}}$
decays and regularity is secured. Here $p$ is the physical pressure and
$\mathcal{P}$ is a pressure moderator of relatively broad forms. The
implications of the results are discussed and regularity criteria in terms of
bounds for $|p+\mathcal{P}|$ within $\Omega$ are deduced. This is joint work with Xinwei Yu.
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Extent |
47 minutes
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Subject | |
Type | |
File Format |
video/mp4
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Language |
eng
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Notes |
Author affiliation: University of St. Andrews
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Series | |
Date Available |
2017-01-27
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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 |
10.14288/1.0340114
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URI | |
Affiliation | |
Peer Review Status |
Unreviewed
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Scholarly Level |
Faculty
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Rights URI | |
Aggregated Source Repository |
DSpace
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Item Media
Item Citations and Data
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International