On the global solvability of the generalised Navier-Stokes system in critical Besov spaces

2025/02/01 by Zhang, Huiyang, Cao, SHiwei, Zhang, Qinghua
#Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2502.00324

Abstract

This paper is devoted to the global solvability of the Navier-Stokes system with fractional Laplacian (-Δ)^α in ℝⁿ for n≥2, where the convective term has the form (|u|^m-1u)⋅∇ u for m≥1. By establishing the estimates for the difference |u₁|^m-1u₁-|u₂|^m-1u₂ in homogeneous Besov spaces, and employing the maximal regularity property of (-Δ)^α in Lorentz spaces, we prove global existence and uniqueness of the strong solution of the Navier-Stokes in critical Besov spaces for both m=1 and m>1

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