Existence and optimal convergence rates of multi-dimensional subsonic potential flows through an infinitely long nozzle with an obstacle inside

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 theoptimalconvergence rates of the flow at far fields via weighted energy estimates and Nash-Moser iteration.