The two‐dimensional stationary Navier–Stokes equations in toroidal Besov spaces

Hiroyuki Tsurumi

Mathematische Nachrichten, 2023, vol. 296, issue 4, 1651-1668

Abstract: We consider the stationary Navier–Stokes equations in the two‐dimensional torus T2$\mathbb {T}^2$. For any ε>0$\varepsilon >0$, we show the existence, uniqueness, and continuous dependence of solutions in homogeneous toroidal Besov spaces Ḃp+ε,q−1+2p(T2)$\dot{B}^{-1+\frac{2}{p}}_{p+\varepsilon , q}(\mathbb {T}^2)$ for given small external forces in Ḃp+ε,q−3+2p(T2)$\dot{B}^{-3+\frac{2}{p}}_{p+\varepsilon , q}(\mathbb {T}^2)$ when 1≤p

Date: 2023
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https://doi.org/10.1002/mana.202000208

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