Stability of the 3D incompressible Navier–Stokes equations with fractional horizontal dissipation

Ruihong Ji, Wen Luo and Liya Jiang

Applied Mathematics and Computation, 2023, vol. 448, issue C

Abstract: The stability problem of Navier–Stokes equations (N–S equations) with fractional dissipation is one of the new areas in Mathematical research. The generalized N–S equations are the equations resulting from replacing −Δ in the N–S equations by (−Δ)α. It has previously been shown that any classical solution of the d-dimensional generalized N–S equations with α≥12+d4 is always global in time. This paper considers the stability problem on the 3D N–S equations with only fractional horizontal dissipation (−Δh)α, where Δh:=∂x12+∂x22. We show that, for any α∈(12,1], the solution corresponding to any sufficiently small initial data in H3(R3) is always global in time and stable in H3(R3). There are many important results on the case when α=1. Our result relaxes this requirement and allows α to go below 1.

Keywords: Stability; N-S equations; Fractional dissipation; Horizontal dissipation (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:448:y:2023:i:c:s0096300323001030

DOI: 10.1016/j.amc.2023.127934

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