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.

中文翻译：

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薄域上的非均匀不可压缩Navier-Stokes方程

我们考虑薄域\（{\ mathbb {T}} ^ 2 \ times \ epsilon {\ mathbb {T}} \），\（\ epsilon \ rightarrow 0 \）上的非均匀不可压缩Navier-Stokes方程。结果表明，\（{\ mathbb {T}} ^ 2 \ times \ epsilon {\ mathbb {T}} \）的弱解收敛于\ D上二维非齐次不可压缩Navier–Stokes方程的强解。 （{\ mathbb {T}} ^ 2 \）作为\（\ epsilon \ rightarrow 0 \）在任意时间间隔上。