Well/ill-posedness for the dissipative Navier–Stokes system in generalized Carleson measure spaces.

As an essential extension of the well known case β ∈ (1/2, 1] to the hyper-dissipative case β ∈ (1, ∞), this paper establishes both well-posedness and ill-posedness (not only norm inflation but also indifferentiability of the solution map) for the mild solutions of the incompressible Navier–Stokes system with dissipation (−Δ)1/2 < β < ∞ through the generalized Carleson measure spaces of initial data that unify many diverse spaces, including the Q space (Q−s = − α)n, the BMO-Sobolev space ( (−Δ)−s/2⁢ BMO)n, the Lip-Sobolev space ( (− Δ)−s/2Lipα)n, and the Besov space (Bs∞, ∞ s)n. [ABSTRACT FROM AUTHOR]