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Global Existence of Strong Solution to 3D Periodic Navier-Stokes Equations

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Submitted:

16 March 2020

Posted:

17 March 2020

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Abstract
The purpose of this paper is to bring to light a method through which the global in time existence for arbitrary large in H1 initial data of a strong solution to 3D periodic Navier-Stokes equations follows. The method consists of subdividing the time interval of existence into smaller sub-intervals carefully chosen. These sub-intervals are chosen based on the hypothesis that for any wavenumber m, one can find an interval of time on which the energy quantized in low-frequency components (up to m) of the solution u is lesser than the energy quantized in high-frequency components (down to m) or otherwise the opposite. We associate then a suitable number m to each one of the intervals and we prove that the norm ||u(t)||H1 is bounded in both mentioned cases. The process can be continued until reaching the maximal time of existence Tmax which yields the global in time existence of strong solution.
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Subject: Computer Science and Mathematics  -   Applied Mathematics
Copyright: This open access article is published under a Creative Commons CC BY 4.0 license, which permit the free download, distribution, and reuse, provided that the author and preprint are cited in any reuse.
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