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On the Topology and Future Stability of the Universe$
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Hans Ringström

Print publication date: 2013

Print ISBN-13: 9780199680290

Published to Oxford Scholarship Online: September 2013

DOI: 10.1093/acprof:oso/9780199680290.001.0001

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Function spaces for distribution functions II: the manifold setting

Function spaces for distribution functions II: the manifold setting

Chapter:
(p.233) 15 Function spaces for distribution functions II: the manifold setting
Source:
On the Topology and Future Stability of the Universe
Author(s):

Hans Ringström

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199680290.003.0015

In order to be able to formulate the Cauchy problem for the Einstein–Vlasov system, it is necessary to define suitable function spaces for the initial datum for the distribution function, as well as for the resulting solution. We do so in Chapter 15. We also define norms for the initial datum in case the initial manifold is compact. Finally, we demonstrate that the stress energy tensor is well defined if the distribution function belongs to the relevant function space.

Keywords:   function spaces, distribution functions, manifolds, norms, cauchy problem, stress energy tensor

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