Stability of Transonic Characteristic Discontinuities in Two-Dimensional Steady Compressible Euler Flows

Abstract

For a two-dimensional steady supersonic Euler flow past a convex cornered wall with right angle, a characteristic discontinuity (vortex sheet and/or entropy wave) is generated, which separates the supersonic flow from the gas at rest (hence subsonic). We proved that such a transonic characteristic discontinuity is structurally stable under small perturbations of the upstream supersonic flow in $BV$. The existence of a weak entropy solution and Lipschitz continuous free boundary (i.e. characteristic discontinuity) is established. To achieve this, the problem is formulated as a free boundary problem for a nonstrictly hyperbolic system of conservation laws; and the free boundary problem is then solved by analyzing nonlinear wave interactions and employing the front tracking method.

arXiv comment26 pages, 3 figures

References in corpus (2)

• Well-Posedness of Transonic Characteristic Discontinuities in Two-Dimensional Steady Compressible Euler Flows
• $L^1$-Stability of Vortex Sheets and Entropy Waves in Steady Compressible Supersonic Euler Flows over Lipschitz Walls

Cited by in corpus (5)

• Well-Posedness of Transonic Characteristic Discontinuities in Two-Dimensional Steady Compressible Euler Flows
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• Stability of supersonic contact discontinuity for two-dimensional steady compressible Euler flows in a finite nozzle
• Stability of transonic jets with strong rarefaction waves for two-dimensional steady compressible Euler system
• Contact discontinuities for 3-D axisymmetric inviscid compressible flows in infinitely long cylinders