Global conic shock wave for the steady supersonic flow past a cone: isothermal case

Dacheng Cui and Huicheng Yin

Vol. 233 (2007), No. 2, 257–289

DOI: 10.2140/pjm.2007.233.257

Abstract

We establish the global existence and stability of a steady symmetric conic shock wave for the perturbed supersonic isothermal flow past an infinitely long circular cone with an arbitrary vertex angle. The flow is assumed to be described by a steady potential equation. By establishing the uniform weighted energy estimate on the linearized problem, we show that the symmetric conic shock attached at the vertex of the cone exists globally in the whole space when the speed of the supersonic incoming flow is appropriately large.

Keywords

isothermal gas, potential equation, supersonic incoming flow, hypersonic flow, conic shock, global existence, tangent vector field

Mathematical Subject Classification 2000

Primary: 35L70, 35L65, 35L67

Secondary: 76N15

Milestones

Received: 19 January 2007

Revised: 27 May 2007

Accepted: 4 September 2007

Published: 1 December 2007