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Solutions of the 3D Navier-Stokes equations for initial data in Ḣ1/2: Robustness of regularity and numerical verification of regularity for bounded sets of initial data in Ḣ1
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Marín-Rubio, Pedro, Robinson, James C. and Sadowski, Witold (2013) Solutions of the 3D Navier-Stokes equations for initial data in Ḣ1/2: Robustness of regularity and numerical verification of regularity for bounded sets of initial data in Ḣ1. Journal of Mathematical Analysis and Applications, Volume 400 (Number 1). pp. 76-85. doi:10.1016/j.jmaa.2012.10.064 ISSN 0022-247X.
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Official URL: http://dx.doi.org/10.1016/j.jmaa.2012.10.064
Abstract
We consider the three-dimensional Navier-Stokes equations on a periodic domain. We give a simple proof of the local existence of solutions in Ḣ1/2, and show that the existence of a regular solution on a bounded time interval [0, T] is stable with respect to perturbations of the initial data in Ḣ1/2 and perturbations of the forcing function in L2(0, T;H-1/2). This forms the key ingredient in a proof that the assumption of regularity for all initial conditions in any given ball in Ḣ1 can be verified computationally in a finite time, strengthening a previous result of Robinson and Sadowski [J.C. Robinson and W. Sadowski, Numerical verification of regularity in the three-dimensional Navier-Stokes equations for bounded sets of initial data, Asymptot.
Item Type: | Journal Article | ||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Journal or Publication Title: | Journal of Mathematical Analysis and Applications | ||||
Publisher: | Academic Press | ||||
ISSN: | 0022-247X | ||||
Official Date: | 1 April 2013 | ||||
Dates: |
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Volume: | Volume 400 | ||||
Number: | Number 1 | ||||
Page Range: | pp. 76-85 | ||||
DOI: | 10.1016/j.jmaa.2012.10.064 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
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