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In this paper, the well-posedness and optimal convergence rates of subsonicirrotational flows through a three dimensional infinitely long nozzle with asmooth obstacle inside are established. More precisely, the global existenceand uniqueness of the uniformly subsonic flow are obtained via variationalformulation 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 theoptimal convergence rates of the flow at far fields via weighted energyestimates and Nash-Moser iteration.

Existence and Optimal Convergence Rates of Multi-dimensional Subsonic Potential Flows Through an Infinitely Long Nozzle with an Obstacle Inside