The Library
Lower bounds on blowing-up solutions of the three-dimensional Navier--Stokes equations in $\dot H^{3/2}$, $\dot H^{5/2}$, and $\dot B^{5/2}_{2,1}$
Tools
Tools
Tools
McCormick, David S., Olson, Eric J., Robinson, James C., Rodrigo Diez, José L., Vidal-López, Alejandro and Zhou, Yi (2016) Lower bounds on blowing-up solutions of the three-dimensional Navier--Stokes equations in $\dot H^{3/2}$, $\dot H^{5/2}$, and $\dot B^{5/2}_{2,1}$. SIAM Journal on Mathematical Analysis, 48 (3). pp. 2119-2132. doi:10.1137/15M1017776 ISSN 0036-1410.
![[img]](https://wrap.warwick.ac.uk/style/images/fileicons/application_pdf.png) |
PDF
WRAP_McCormick_15m1017776.pdf - Published Version - Requires a PDF viewer. Download (717Kb) |
Official URL: http://dx.doi.org/10.1137/15M1017776
Abstract
If u is a smooth solution of the Navier–Stokes equations on R
3 with first blowup time T, we prove lower bounds for u in the Sobolev spaces H˙ 3/2 , H˙ 5/2 , and the Besov space B˙ 5/2 2,1 , with optimal rates of blowup: we prove the strong lower bounds ku(t)kH˙ 3/2 ≥ c(T − t) −1/2 and ku(t)kB˙ 5/2 2,1 ≥ c(T − t) −1 , but in H˙ 5/2 we only obtain the weaker result lim supt→T − (T −t)ku(t)kH˙ 5/2 ≥ c. The
proofs involve new inequalities for the nonlinear term in Sobolev and Besov spaces, both of which are obtained using a dyadic decomposition of u.
| Item Type: | Journal Article | ||||||||
|---|---|---|---|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||
| Library of Congress Subject Headings (LCSH): | Navier-Stokes equations | ||||||||
| Journal or Publication Title: | SIAM Journal on Mathematical Analysis | ||||||||
| Publisher: | Society for Industrial and Applied Mathematics | ||||||||
| ISSN: | 0036-1410 | ||||||||
| Official Date: | 14 April 2016 | ||||||||
| Dates: |
|
||||||||
| Volume: | 48 | ||||||||
| Number: | 3 | ||||||||
| Number of Pages: | 20 | ||||||||
| Page Range: | pp. 2119-2132 | ||||||||
| DOI: | 10.1137/15M1017776 | ||||||||
| Status: | Peer Reviewed | ||||||||
| Publication Status: | Published | ||||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||||
| Description: | |||||||||
| Date of first compliant deposit: | 19 April 2016 | ||||||||
| Date of first compliant Open Access: | 12 August 2016 | ||||||||
| Funder: | Engineering and Physical Sciences Research Council (EPSRC), European Research Council (ERC) | ||||||||
| Grant number: | EP/G007470/1, EP/G007470/1 (EPSRC), 616797. (ERC) | ||||||||
| Adapted As: | |||||||||
| Open Access Version: |
Request changes or add full text files to a record
Repository staff actions (login required)
 |
View Item |
Downloads
Downloads per month over past year
