miun.sePublications
Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Shock Waves in Plane Symmetric Spacetimes
Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering and Sustainable Development.
2008 (English)In: Communications in Partial Differential Equations, ISSN 0360-5302, Vol. 33, no 11, 2020-2039 p.Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
2008. Vol. 33, no 11, 2020-2039 p.
National Category
Mathematics Natural Sciences
Identifiers
URN: urn:nbn:se:miun:diva-8302DOI: 10.1080/03605300802421948ISI: 000260833800005Scopus ID: 2-s2.0-56049117658OAI: oai:DiVA.org:miun-8302DiVA: diva2:134134
Note
VR-MathematicsAvailable from: 2009-01-18 Created: 2009-01-18 Last updated: 2009-11-02Bibliographically approved

Open Access in DiVA

No full text

Other links

Publisher's full textScopus

Search in DiVA

By author/editor
Ståhl, Fredrik
By organisation
Department of Engineering and Sustainable Development
In the same journal
Communications in Partial Differential Equations
MathematicsNatural Sciences

Search outside of DiVA

GoogleGoogle Scholar

Altmetric score

Total: 76 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf