Stability of stationary solutions to the Navier–Stokes equations in the Besov space

Hideo Kozono and Senjo Shimizu

Mathematische Nachrichten, 2023, vol. 296, issue 5, 1964-1982

Abstract: We consider the stability of the stationary solution w of the Navier–Stokes equations in the whole space Rn$\mathbb {R}^n$ for n≥3$n \ge 3$. It is clarified that if w is small in Ḃp*,q′−1+np*$\dot{B}^{-1+\frac{n}{p_\ast }}_{p_\ast , q^{\prime }}$ for 1≤p* 0$s > 0$.

Date: 2023
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