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<p>We are concerned with the shock formation to one-dimensional isentropic and momentum-energy systems of relativistic Euler equations. We first use characteristics theory to obtain the solution of the blow up equations; this solution can be extended beyond the explosion time. According to the singularity of the characteristic transformation, then we construct the first-order approximation solution and obtain some estimates near the blow up point. Based on the first-order approximation solution, a linear iteration scheme is constructed to obtain the compactness of the approximation solution’s sequence, and the convergence of the approximation solutions is inductively proved. Finally, we prove the difference between two solutions of entropy and momentum-energy systems and consider the non-relativistic limits.</p>

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Shock formation and construction to the \(2\times 2\) relativistic Euler equations and non-relativistic limit of relativistic Euler equations

  • 期刊论文

  • 发表日期：

    2025年2月19日

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  • Yongcai Geng

摘要

We are concerned with the shock formation to one-dimensional isentropic and momentum-energy systems of relativistic Euler equations. We first use characteristics theory to obtain the solution of the blow up equations; this solution can be extended beyond the explosion time. According to the singularity of the characteristic transformation, then we construct the first-order approximation solution and obtain some estimates near the blow up point. Based on the first-order approximation solution, a linear iteration scheme is constructed to obtain the compactness of the approximation solution’s sequence, and the convergence of the approximation solutions is inductively proved. Finally, we prove the difference between two solutions of entropy and momentum-energy systems and consider the non-relativistic limits.