Relativistic Euler equations for isentropic fluids: Stability of Riemann solutions with large oscillation
Relativistic Euler equations for isentropic fluids: Stability of Riemann solutions with large oscillation
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DOI：
10.1007/s00033-004-3097-9
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发表时间：
2004-11
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影响因子：
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通讯作者：
Gui-Qiang G. Chen;Yachun Li
中科院分区：
文献类型：
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作者：
Gui-Qiang G. Chen;Yachun Li
在狭义相对论中分析了等熵流体的2 × 2相对论欧拉方程的全局熵解，建立了l∞∩bvlocy上具有任意大振荡的熵解类Riemann解的唯一性。唯一性结果不需要具体参考构造熵解的任何特定方法。那么黎曼解的唯一性意味着黎曼初始数据在任意大的1∩L∞∩bv摄动下黎曼解的无粘时间渐近稳定性，前提是对应的解在L∞上且具有局部有界全变分，允许时间线性增长。将此方法推广到具有任意大振荡的l∞熵解类中包含真空的Riemann解的稳定性问题。
We analyze global entropy solutions of the 2 × 2 relativistic Euler equations for isentropic fluids in special relativity and establish the uniqueness of Riemann solutions in the class of entropy solutions inL∞∩BVlocwith arbitrarily large oscillation. The uniqueness result does not require specific reference to any particular method for constructing the entropy solutions. Then the uniqueness of Riemann solutions implies their inviscid time-asymptotic stability under arbitrarily largeL1∩L∞∩BVlocperturbation of the Riemann initial data, provided that the corresponding solutions are inL∞and have local bounded total variation that allows the linear growth in time. This approach is also extended to deal with the stability of Riemann solutions containing vacuum in the class of entropy solutions inL∞with arbitrarily large oscillation.