Global solutions to 3D incompressible Navier–Stokes equations with some large initial data. (July 2022)

• Record Type: Journal Article
• Authors: Yu, Yanghai; Li, Jinlu; Yin, Zhaoyang
• Is Part Of: Applied mathematics letters. Volume 129(2022)
• Publication Date: 2022-07
• Subjects: Incompressible Navier–Stokes equations -- Large solution; Applied mathematics -- Periodicals; 519.05
• DOI: 10.1016/j.aml.2022.107954
• Languages: English
• ISSNs: 0893-9659

Abstract

Abstract: In this paper, we derive a new smallness hypothesis of initial data for the three-dimensional incompressible Navier–Stokes equations. More precisely, we prove that if ‖ u 0 1 + u 0 2 ‖ B ̇ p, 1 3 p − 1 + ‖ u 0 3 ‖ B ̇ p, 1 3 p − 1 ‖ u 0 1 ‖ B ̇ p, 1 3 p − 1 + ‖ u 0 2 ‖ B ̇ p, 1 3 p − 1 × exp C ( ‖ u 0 ‖ B ̇ ∞, 2 − 1 2 + ‖ u 0 ‖ B ̇ ∞, 1 − 1 ) is small enough, the Navier–Stokes equations have a unique global solution. As an application, we construct two examples of initial data satisfying the smallness condition, but whose B ̇ ∞, ∞ − 1 ( R 3 ) norm can be arbitrarily large.