Entropy solutions of the Euler equations for isothermal relativistic fluids
Entropy solutions of the Euler equations for isothermal relativistic fluids
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DOI：
10.1504/ijdsde.2007.013742
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发表时间：
2007-01
影响因子：
0.3
通讯作者：
P. LeFloch;M. Yamazaki
中科院分区：
文献类型：
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作者：
P. LeFloch;M. Yamazaki
我们研究了相对论性等温理想流体Euler方程的初值问题，推广了LeFloch和Shelukhin在非相对论性条件下的一个解的存在性结果.我们建立了全局定义，有界可测，熵解的存在性与任意大振幅。Smoller和Temple的早期结果涵盖了避免真空状态的有界变差的解决方案。我们的新框架在更大的函数空间中提供了解决方案，并允许质量密度消失，速度场接近光速。相对论性欧拉方程在这两种状态下都变得强烈退化，因为保守变量或通量变量消失或爆炸。我们的证明是基于补偿紧性的方法，并利用了欧拉方程的标度不变性。
We investigate the initial-value problem for the relativistic Euler equations of isothermal perfect fluids, and generalise an existence result due to LeFloch and Shelukhin for the non-relativistic setting. We establish the existence of globally defined, bounded measurable, entropy solutions with arbitrary large amplitude. An earlier result by Smoller and Temple covered solutions with bounded variation that avoid the vacuum state. Our new framework provides solutions in a larger function space and allows for the mass density to vanish and the velocity field to approach the light speed. The relativistic Euler equations become strongly degenerate in both regimes, as the conservative or the flux variables vanish or blow up. Our proof is based on the method of compensated compactness and takes advantage of a scaling invariance property of the Euler equations.