2020/04/15 by Abdelkerim Châabani, Chaabani, Abdelkerim
Engineering · Mathematics · #Advanced Mathematical Physics Problems #FOS: Mathematics #General Mathematics (math.GM) #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations #primary 35A01 secondary 35D35
paper · pdf · doi:10.48550/arxiv.2004.06956
openalex publication_date 2020/04/15 · openalex created_date 2020/04/24 · openalex updated_date 2026/07/28
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.