| In this work, we give a perturbation theorem for strong polynomial solutions to the zero surface tension Hele-Shaw flows to enable us to see more about solutions which are not polynomials but are close to them. Many applications of this theorem are given. In the suction case, we obtain some interesting results regarding blow-up time; In the injection case, we obtain precise large-time rescaling behaviors for large-data to Hele-Shaw flows in terms of Richardson complex moments. A shorter proof of short-time well-posedness result is given as a byproduct of this theorem. |
