Local existence with physical vacuum boundary condition to Euler equations with damping

In this paper, we consider the local existence of solutions to Euler equations with linear damping under the assumption of physical vacuum boundary condition. By using the transformation introduced in Lin and Yang (Methods Appl. Anal. 7 (3) (2000) 495) to capture the singularity of the boundary, we prove a local existence theorem on a perturbation of a planar wave solution by using Littlewood–Paley theory and justifies the transformation introduced in Liu and Yang (2000) in a rigorous setting.