Work

Improved regularity and analyticity of Cannone-Karch solutions of the three-dimensional Navier–Stokes equations on the torus

Year: 2024

Type: article

Abstract: We consider the three-dimensional Navier–Stokes equations, with initial data having second derivatives in the space of pseudomeasures. Solutions of this system with such data have been shown to exist previously by Cannone and Karch. As the Navier–Stokes equations are a parabolic system, the solutions gain regularity at positive times. We demonstrate an improved gain of regularity at positive times as compared to that demonstrated by Cannone and Karch. We further demonstrate that the solutions are analytic at all positive times, with lower bounds given for the radius of analyticity.

Source: Monatshefte für Mathematik

DOI: 10.1007/s00605-024-02012-7

Authors: David M. Ambrose, Milton C. Lopes Filho, Helena J. Nussenzveig Lopes

Institutions: Drexel University, Universidade Federal do Rio de Janeiro

Language: English

Topic: Navier-Stokes equation solutions

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,990

Funders: National Science Foundation, Conselho Nacional de Desenvolvimento Científico e Tecnológico, Fundação Carlos Chagas Filho de Amparo à Pesquisa do Estado do Rio de Janeiro, Directorate for Mathematical and Physical Sciences