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

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Original languageEnglish
Pages (from-to)217-231
Journal / PublicationJournal of Differential Equations
Issue number1
Publication statusPublished - 1 Mar 2005


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. © 2004 Elsevier Inc. All rights reserved.

Research Area(s)

  • Euler equations, Littlewood-Paley theory, Local existence, Physical vacuum boundary condition