In a two-dimensional bounded domain $$\Omega $$ , we consider the system of Navier–Stokes equations describing the flow of a viscous compressible gas with no allowance for heat exchange with the ambient medium under small variations of density in the equations of motion. We prove the existence of a solution to the problem of exact local controllability of this system by an external force supported in an arbitrary fixed subdomain $$\omega \subset \Omega $$ .

中文翻译：

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二维粘性气流的精确局部可控性

在二维有界域 $$\Omega $$ 中，我们考虑描述粘性可压缩气体流动的 Navier-Stokes 方程组，在密度变化很小的情况下，不考虑与周围介质的热交换运动。我们证明了通过在任意固定子域 $$\omega \subset \Omega $$ 中支持的外力来解决该系统的精确局部可控性问题的解决方案的存在。