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MiS Preprint

Singular solutions for the Uehling-Uhlenbeck equation

Miguel Escobedo, Stephane Mischler and Juan J.L. Velazquez


In this paper we prove the existence of solutions of the Uehling-Uhlenbeck equation that behave like k^(-7/6) as k tends to zero. 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 [5].

MSC Codes:
35Q40, 82C10
kinetic equation, singular solutions

Related publications

2008 Repository Open Access
M. Escobedo, S. Mischler and Juan J. L. Velázquez

Singular solutions for the Uehling-Uhlenbeck equation

In: Proceedings of the Royal Society of Edinburgh / A, 138 (2008) 1, pp. 67-107