Preprint Article Version 2 This version is not peer-reviewed

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

Version 1 : Received: 16 March 2020 / Approved: 17 March 2020 / Online: 17 March 2020 (15:50:42 CET)
Version 2 : Received: 23 March 2020 / Approved: 24 March 2020 / Online: 24 March 2020 (03:33:43 CET)

How to cite: Chaabani, A. Global in Time Existence of Strong Solution to 3D Navier-Stokes Equations. Preprints 2020, 2020030278 (doi: 10.20944/preprints202003.0278.v2). Chaabani, A. Global in Time Existence of Strong Solution to 3D Navier-Stokes Equations. Preprints 2020, 2020030278 (doi: 10.20944/preprints202003.0278.v2).

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.

Subject Areas

Navier Stokes; strong solution; global existence

Comments (1)

Comment 1
Received: 24 March 2020
Commenter: Abdelkerim Chaabani
Commenter's Conflict of Interests: Author
Comment: I improved the language. I also corrected some misprints and some mistakes that are due to my clumsiness (I repeat my apologies). I added few lines to the discussion (concerning an important observation). I replaced t by t-t_0 in some lines (integration error).
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