Blow-up rate estimates for weak solutions of the Navier-Stokes equations
Chen, Zhi-Min and Price, W.G. (2001) Blow-up rate estimates for weak solutions of the Navier-Stokes equations. Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 457, (2015), 2625-2642. (doi: 10.1098/rspa.2001.0854).
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Description/Abstract
The interior regularity problem for the Leray weak solutions u of the Navier—Stokes equations in a domain z ² Rn with n > 3 is investigated. It is shown that u is regular in a neighbourhood of a point (x0,t0) ] z 2 (0, T) if there exist constants 0 h &thetas; < 1 and small k > 0 such that lim ess sup |t – t0|&thetas;/2|x – x0|1-&thetas; |u(x,t)| < k
kMXQ1/k(xo,to) with Q1/k (x0,t0) = {x ] Rn; |x – x0 < 1/k} 2 (t0 – 1/k2,t0 + 1/k2). If (x0,t0) is an irregular point of u, there exists a sequence of non-zero measure sets Eki ² Q1/ki (x0,t0) for i = 1,2,..., such that the blow-up rate estimate |u(x,t)| > k|t – t0|-&thetas;/2|x – x 0|-1+&thetas;,(x,t) ] Eki holds.
| Item Type: | Article |
|---|---|
| ISSNs: | 1364-5021 (print) |
| Related URLs: | |
| Keywords: | Navier-Stokes equations, weak, solutions, interior, regularity, Lorentz, spaces |
| Subjects: | Q Science > QA Mathematics |
| Divisions: | University Structure - Pre August 2011 > School of Engineering Sciences |
| Item ID: | 21786 |
| Date Deposited: | 16 Mar 2006 |
| Last Modified: | 01 Jun 2011 11:08 |
| Contributors: | Chen, Zhi-Min (Author) Price, W.G. (Author) |
| Date: | 2001 |
| Status: | Published |
| Contact Email Address: | zhimin@ship.soton.ac.uk |
| URI: | http://eprints.soton.ac.uk/id/eprint/21786 |
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