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Singular solutions for the Uehling–Uhlenbeck equation

Published online by Cambridge University Press:  05 February 2008

M. Escobedo ,
S. Mischler  and
J. J. L. Velázquez
M. Escobedo
Affiliation:
Departamento de Matemáticas, Universidad del País Vasco, Apartado 644, 48080 Bilbao, Spain ([email protected])
S. Mischler
Affiliation:
Ceremade, Université Paris IX-Dauphine, place du Maréchal de Lattre de Tasigny, 75016 Paris, France ([email protected])
J. J. L. Velázquez
Affiliation:
Departamento de Matemática Aplicada, Facultad de Matemáticas, Universidad Complutense, 28040 Madrid, Spain (jj\[email protected])
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Abstract

In this paper we prove the existence of solutions of the Uehling–Uhlenbeck equation that behave like $k^{-7/6}$ as $k\to0$. From the physical point of view, such solutions can be thought as particle distributions in the space of momentum having a sink (or a source) of particles with zero momentum. Our construction is based on the precise estimates of the semigroup for the linearized equation around the singular function $k^{-7/6}$ that we obtained in an earlier paper.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 138 , Issue 1 , February 2008 , pp. 67 - 107
Copyright
2008 Royal Society of Edinburgh

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