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

2024/02/01 by David M. Ambrose, Ambrose, David M., Milton C. Lopes Filho +3 · 1 citation
Engineering · #76D05 35B65 35K45 76D03 #Advanced Numerical Methods in Computational Mathematics #Analysis of PDEs (math.AP) #FOS: Mathematics #Stability and Controllability of Differential Equations #Vibration and Dynamic Analysis

paper · pdf · doi:10.48550/arxiv.2402.01038

openalex publication_date 2024/02/01 · openalex created_date 2024/02/06 · openalex updated_date 2026/07/28

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.

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