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

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.