On the convergence rates of multi-dimensional subsonic irrotational flows in unbounded domains

This paper is concerned with the convergence rates of subsonic flows for airfoil problem and infinite long largely-open nozzle problem, which is an improvement of [7,11,15,20]. The maximum principle is applied to estimate the potential function, by choosing the proper compared functions. Then, by the weighted Schauder estimates, the convergence rates of velocity at the far field are shown as $|x|^{-n+1}$. Furthermore, we construct the examples to show the optimality of our convergence rates and the expansion of the incompressible airfoil flow at infinity, indicating the higher convergence rates $|x|^{-n}$.