Archive for Rational Mechanics and Analysis

, Volume 221, Issue 2, pp 559–602 | Cite as

Two Dimensional Subsonic Euler Flows Past a Wall or a Symmetric Body

Article

Abstract

The existence and uniqueness of two dimensional steady compressible Euler flows past a wall or a symmetric body are established. More precisely, given positive convex horizontal velocity in the upstream, there exists a critical value \({\rho_{\rm cr}}\) such that if the incoming density in the upstream is larger than \({\rho_{\rm cr}}\), then there exists a subsonic flow past a wall. Furthermore, \({\rho_{\rm cr}}\) is critical in the sense that there is no such subsonic flow if the density of the incoming flow is less than \({\rho_{\rm cr}}\). The subsonic flows possess large vorticity and positive horizontal velocity above the wall except at the corner points on the boundary. Moreover, the existence and uniqueness of a two dimensional subsonic Euler flow past a symmetric body are also obtained when the incoming velocity field is a general small perturbation of a constant velocity field and the density of the incoming flow is larger than a critical value. The asymptotic behavior of the flows is obtained with the aid of some integral estimates for the difference between the velocity field and its far field states.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Chao Chen
    • 1
  • Lili Du
    • 2
  • Chunjing Xie
    • 3
  • Zhouping Xin
    • 4
  1. 1.School of Mathematics and Computer ScienceFujian Normal UniversityFuzhouPeople’s Republic of China
  2. 2.Department of MathematicsSichuan UniversityChengduPeople’s Republic of China
  3. 3.Department of Mathematics, Institute of Natural SciencesMinistry of Education Key Laboratory of Scientific and Engineering Computing, SHL-MAC, Shanghai Jiao Tong UniversityShanghaiPeople’s Republic of China
  4. 4.The Institute of Mathematical Sciences and Department of MathematicsThe Chinese University of Hong KongShatinHong Kong

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