The expansion of supersonic flows into a vacuum through a convex duct with limited length. (English) Zbl 1411.35200
The authors study the two-dimensional steady supersonic isentropic compressible Euler flow through a convex duct of limited length. The steady Euler system governs the density \(\rho\) and two-dimensional velocity \((u,v)\), with pressure \(p=\rho^\gamma\), \(1\leq\gamma\leq 5/3\). The variables’ values ath the entrance of the duct are given (with supersonic velocity \(u\)). The duct is symmetrical with respect to the \(x\) axis and is convex, and also the turning angle of the walls is less than the critical value of the incoming flow. The authors prove the existence of continuous piecewise smooth solution of the flow that expands into the vacuum.
Reviewer: Ilya A. Chernov (Petrozavodsk)
MSC:
| 35L65 | Hyperbolic conservation laws |
| 35J70 | Degenerate elliptic equations |
| 35R35 | Free boundary problems for PDEs |
| 35J65 | Nonlinear boundary value problems for linear elliptic equations |
| 76J20 | Supersonic flows |
| 35Q31 | Euler equations |
Keywords:
rarefaction waves; Goursat problem; mixed boundary value problem; centered wave problem; vacuum state; existence of solution; smoothness; isentropic compressible Euler flowReferences:
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