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