In this paper, the well-posedness and optimal convergence rates of subsonic irrotational flows through a three dimensional infinitely long nozzle with a smooth obstacle inside are established. More precisely, the global existence and uniqueness of the uniformly subsonic flow are obtained via variational formulation as long as the incoming mass flux is less than a critical value. Furthermore, with the aid of delicate choice of weight functions, we prove the optimal convergence rates of the flow at far fields via weighted energy estimates and Nash-Moser iteration.

中文翻译：

---

内有障碍物的无限长喷管多维亚音速势流的存在性和最优收敛率

本文建立了亚音速无旋流通过内部有光滑障碍物的三维无限长喷嘴的适定性和最优收敛率。更准确地说，只要传入质量通量小于临界值，均匀亚音速流动的全局存在性和唯一性是通过变分公式获得的。此外，借助权重函数的精细选择，我们通过加权能量估计和 Nash-Moser 迭代证明了远场流的最佳收敛速度。