On the Cauchy problem for hyperdissipative Navier–Stokes equations in super-critical Besov and Triebel–Lizorkin spaces. (January 2023)

• Record Type: Journal Article
• Authors: Baaske, Franka; Schmeisser, Hans-Jürgen
• Is Part Of: Nonlinear analysis. Volume 226(2023)
• Publication Date: 2023-01
• Subjects: 46E35 -- 35K25 -- 35K55 -- 35Q35; Hyperdissipative Navier–Stokes equations -- Mild and strong solutions -- Supercritical function spaces of Besov and Triebel–Lizorkin type -- Well-posedness; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2022.113140
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper, we study well-posedness of the Cauchy problem for hyperdissipative Navier–Stokes equations with initial data in super-critical Besov and Triebel–Lizorkin spaces. We prove existence and uniqueness of mild and strong solutions which are local in time.