Inhomogeneous Incompressible Navier–Stokes Equations on Thin Domains

Abstract

We consider the inhomogeneous incompressible Navier–Stokes equation on thin domains $${\mathbb {T}}^2 \times \epsilon {\mathbb {T}}$$, $$\epsilon \rightarrow 0$$. It is shown that the weak solutions on $${\mathbb {T}}^2 \times \epsilon {\mathbb {T}}$$ converge to the strong/weak solutions of the 2D inhomogeneous incompressible Navier–Stokes equations on $${\mathbb {T}}^2$$ as $$\epsilon \rightarrow 0$$ on arbitrary time interval.