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Hash: SHA512

PGP Public Key:
0x110881E017DE96C19332288E9F42887758CE8626

Warrant Canary:
2026-10-07

[Submitted on 6 Oct 2026]

Preprint:
A Hartman-Grobman Theorem for the Navier-Stokes Equation on T³

Contributors: Rongchang Liu, Kening Lu, Lin Shi

arXiv: arxiv.org/abs/2610.08058
DOI:   doi.org/10.48550/arXiv.2610.08058

PDF:   arxiv.org/pdf/2610.08058

Submission history:
From: Kening Lu
[v1] Tue, 6 Oct 2026 09:55:46 UTC (62 KB)

Abstract:

We prove a local Hartman-Grobman theorem at zero for the unforced Navier-Stokes equation on the three-dimensional torus in the strong topology of Hs for every s>7/2. More precisely, we construct a homeomorphism between open positively invariant neighborhoods of zero that conjugates the Navier-Stokes semiflow to the heat semigroup. We develop an infinite-dimensional boundary-time scheme built on a nested hierarchy of exact asymptotic dynamical factors. Their fiber geometry yields Sobolev block coordinates with autonomous finite-dimensional factor systems, on which boundary-time topological conjugacies can be constructed at every finite level and then assembled on a common neighborhood into the desired Hs conjugacy. The infinite-dimensional assembly relies on new spectral estimates for the divergence-free transport structure, which control derivative loss and the blockwise tails of the finite-level conjugacies and their inverses without an additional spectral-gap assumption.

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