Existence and uniqueness of analytic solution for unsteady crystals with zero surface tension

We study the initial value problem for two-dimensional dendritic crystal growth with zero surface tension. If the initial data is analytic and close to Ivantsov steady solution, it is proved that unique analytic solution exists locally in time. The analysis is based on a Nirenberg Theorem on abstract Cauchy–Kovalevsky problem in properly chosen Banach spaces.