Steady supersonic flows past Lipschitz wedges for two-dimensional relativistic Euler equations. (English) Zbl 07906784
Summary: We are concerned with two-dimensional steady supersonic flows past Lipschitz wedges for the relativistic Euler equations. If the vertex angle of the upstream flow is less than the critical angle, determined by shock polar, then a shock wave is generated from the wedge vertex. When the total variations of the tangent angle of the boundary and the upstream flow are both suitably small, we establish global stability of entropy solutions, including a large 1-shock wave. Moreover, we obtain global nonrelativistic limits of the entropy solutions, and also investigate the asymptotic behavior of these solutions as \(x\to +\infty\). It is worth mentioning that we demonstrate the basic properties of nonlinear waves for the two-dimensional steady relativistic Euler system, especially the geometric structure of shock polar.
MSC:
| 35Q31 | Euler equations |
| 76J20 | Supersonic flows |
| 76L05 | Shock waves and blast waves in fluid mechanics |
| 76N10 | Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics |
| 76Y05 | Quantum hydrodynamics and relativistic hydrodynamics |
| 83A05 | Special relativity |
| 35B35 | Stability in context of PDEs |
| 35B40 | Asymptotic behavior of solutions to PDEs |
| 35L65 | Hyperbolic conservation laws |
| 35L67 | Shocks and singularities for hyperbolic equations |
| 35A01 | Existence problems for PDEs: global existence, local existence, non-existence |
| 35A02 | Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness |
Keywords:
steady relativistic Euler equations; shock wave; wave front tracking method; interaction of waves; asymptotic behaviorReferences:
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