Asymptotic stability of stationary Navier–Stokes flow in Besov spaces

Article type: Research Article

Authors: Cunanan, Jayson^a | Okabe, Takahiro^b | Tsutsui, Yohei^{c; *}

Affiliations: [a] Department of Mathematics, Saitama University, Saitama, Japan. E-mail: [email protected] | [b] Graduate School of Engineering Science, Osaka University, Osaka, Japan. E-mail: [email protected] | [c] Department of Mathematics, Kyoto University, Kyoto, Japan. E-mail: [email protected]

Correspondence: [*] Corresponding author. E-mail: [email protected].

Abstract: We discuss the asymptotic stability of stationary solutions to the incompressible Navier–Stokes equations on the whole space in Besov spaces. A critical estimate for the semigroup generated by the Laplacian with a perturbation is the main ingredient of the argument.

Keywords: Asymptotic stability, incompressible Navier–Stokes equations, Besov spaces

DOI: 10.3233/ASY-211720

Journal: Asymptotic Analysis, vol. 129, no. 1, pp. 29-50, 2022