Global solution of the 3‐D incompressible Navier‐Stokes equations in the Besov spaces B˙r1, r2, r3σ, 1. (12th July 2017)

• Record Type: Journal Article
• Authors: Ru, Shaolei; Chen, Jiecheng
• Is Part Of: Mathematical methods in the applied sciences. Volume 40:Number 18(2018)
• Page Start: 6790
• Page End: 6800
• Publication Date: 2017-07-12
• Subjects: global well‐posedness -- Navier‐Stokes equations -- smoothing effect; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.4493
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : In this paper, we construct a more general Besov spaces B ˙ r 1, r 2, r 3 σ, q and consider the global well‐posedness of incompressible Navier‐Stokes equations with small data in B ˙ r 1, r 2, r 3 σ, ∞ for 1 r 1 + 1 r 2 + 1 r 3 − σ = 1, 1 ⩽ r i < ∞ . In particular, we show that for any 2 γ + 1 p 1 + 1 p 2 + 1 p 3 − s = 1, 1 < γ < ∞ and r i ⩽ p i < ∞, the solution with initial data in B ˙ r 1, r 2, r 3 σ, ∞ belong to L ˜ γ [ 0, T ), B ˙ p 1, p 2, p 3 s, ∞, which, as far as we know, has not been discussed in other papers. Moreover, the smoothing effect of the solution to Navier‐Stokes equations is proved, which may have its own interest.