Abstract
We study the singularity formation of smooth solutions of the relativistic Euler equations in (3+1)-dimensional spacetime for infinite initial energy. We prove that the smooth solution blows up in finite time provided that the radial component of the initial generalized momentum is sufficiently large without the conditions \(M(0)>0\) and \(s^{2}<\frac{1}{3}c^{2}\), which were two key constraints stated in Pan and Smoller (Commun Math Phys 262:729–755, 2006).
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Acknowledgements
The authors acknowledge support from the Natural Science Foundation of Henan Province Science and Technology Department (162300410077), the Youth Natural Science Foundation of Zhengzhou University of Aeronautics (2015113001), the Project of Youth Backbone Teachers of Colleges and Universities in Henan Province (2013GGJS-142) and NSFC(11501525).
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Dong, J., Zhu, J. A note on blowup of smooth solutions for relativistic Euler equations with infinite initial energy. Lett Math Phys 108, 2479–2485 (2018). https://doi.org/10.1007/s11005-018-1082-z
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DOI: https://doi.org/10.1007/s11005-018-1082-z