Half-space problems for steady gas flows with evaporation and condensation have been studied analytically and numerically [1–3].In the half-space problems,evaporation or condensation can take place only when macroscopic variables at infinity and on the condensed phase satisfy certain relations.It is practically important that the relations are used as boundary conditions for fluid-dynamic equations at the vapor-liquid interface for small Knudsen numbers.These studies however have not examined the case where the evaporation and condensation at the interface take place periodically.Therefore,there remains a question about an e ect of time-periodic evaporation and condensation flows.