Vol. 233, No. 2, 2007

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ISSN: 0030-8730
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

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.

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
Received: 19 January 2007
Revised: 27 May 2007
Accepted: 4 September 2007
Published: 1 December 2007
Dacheng Cui
Department of Mathematics
Nanjing University
Nanjing, 210093
Huicheng Yin
Department of Mathematics
Nanjing University
Nanjing, 210093