2025/09/19 by Qixiang Yang, Hongwei Li, Yang, Qixiang +1
Mathematics · #35Q30 #42B35 #46E30 #76D03 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions
paper · pdf · doi:10.48550/arxiv.2509.15663
openalex publication_date 2025/09/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29
The properties of solutions to Navier-Stokes equations, including well-posedness and Gevrey regularity, are a class of highly interesting problems. We are inspired by the location result on Triebel-Lizorkin-Lorentz space of Hobus and Saal in 2019. In order to overcome the difficulties they encountered when dealing with global well-posedness, we introduce the single norm iterative space m'm F(n)/(p)-1,qp,r and utilize tools such as the Fefferman-Stein inequality to investigate the properties of our iterative spaces. As a result, we establish the global well-posedness of Navier-Stokes equations in critical Triebel-Lizorkin-Lorentz space and obtain the Gevrey regularity of the mild solution. Regarding that there're many regularity studies focused on Besov spaces, such as Bae-Biswas-Tadmor(2012) and Liu-Zhang (2024), our Triebel-Lizorkin-Lorentz spaces contain more general initial value spaces, including part of Besov spaces and all of Triebel-Lizorkin spaces, etc.. Furthermore, compared with Germain-Pavlović-Staffilani (2007), our Gevrey estimation also implies spatial analyticity and is more convenient to unify the estimates of gradient of any order.