Work

Global well-posedness of the 3D Navier-Stokes equations with helical $L^1$ vorticity

Year: 2026

Type: preprint

Abstract: We show that the Navier-Stokes equations on $\mathbb R^2\times\mathbb T$ are globally well posed for initial vorticities that are both helically symmetric and integrable. This class of data typically generates velocity fields of infinite kinetic energy, so this result is not covered by the classical finite-energy well-posedness theory. This result is supercritical from the perspective of the three-dimensional Navier-Stokes scaling, and it is made possible by the special structure of helical flows using time-weighted Kato-type spaces.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.05193

Authors: Gancedo, Francisco, Hidalgo-Torné, Antonio

Language: English

Topic: Navier-Stokes equation solutions

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Max-Planck-Institut für Mathematik in den Naturwissenschaften, Agencia Estatal de Investigación

Awards: G1175115578, G1243386076, G2262748287, G294895050, G300979063, G3480869486, G3681338154, G4025565791, G425668148, G5080475149, G7084143925

OpenAlex ID: W7211874409

Cites: 2

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Related to: 10