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  Shock Waves in Plane Symmetric Spacetimes

Rendall, A. D., & Stahl, F. (2008). Shock Waves in Plane Symmetric Spacetimes. Communications in Partial Differential Equations, 33(11), 2020-2039. doi:10.1080/03605300802421948.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-1382-E Version Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-1385-8
Genre: Journal Article

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ComPDE33_2020.pdf (Publisher version), 144KB
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 Creators:
Rendall, Alan D.1, Author              
Stahl, Fredrik2, Author
Affiliations:
1Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, Golm, DE, ou_24012              
2External Organizations, ou_persistent22              

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 Abstract: We consider Einstein's equations coupled to the Euler equations in plane symmetry, with compact spatial slices and constant mean curvature time. We show that for a wide variety of equations of state and a large class of initial data, classical solutions break down in finite time. The key mathematical result is a new theorem on the breakdown of solutions of systems of balance laws. We also show that an extension of the solution is possible if the spatial derivatives of the energy density and the velocity are bounded, indicating that the breakdown is really due to the formation of shock waves.

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 Dates: 2008-11
 Publication Status: Published online
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 Rev. Method: Peer
 Identifiers: DOI: 10.1080/03605300802421948
eDoc: 362686
arXiv: 0806.1597
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Title: Communications in Partial Differential Equations
Source Genre: Journal
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Pages: - Volume / Issue: 33 (11) Sequence Number: - Start / End Page: 2020 - 2039 Identifier: ISSN: 1532-4133