Global Navier-Stokes flows in intermediate spaces

• DOI: 10.1016/j.jde.2025.02.025
• Publication Date: 2025-02-18T12:05:15Z
• Authors: Zachary Bradshaw; Misha Chernobai; Tai-Peng Tsai
• Keywords: Mathematics - Analysis of PDEs; FOS: Mathematics; 35Q30, 76D03, 76D05; Analysis of PDEs (math.AP)

We construct global weak solutions of the three dimensional incompressible Navier-Stokes equations in intermediate spaces between the space of uniformly locally square integrable functions and Herz-type spaces which involve weighted integrals centered at the origin. Our results bridge the existence theorems of Lemarié-Rieusset and of Bradshaw, Kukavica and Tsai. An application to eventual regularity is included which generalizes the prior work of Bradshaw, Kukavica and Tsai as well as Bradshaw, Kukavica and Ozanski.<br/>We moved Lemma 3.1 to Lemma 2.1, and added Lemma 2.11 and several references<br/>