Journal of Statistical Physics

, Volume 138, Issue 4, pp 838–875

Well-Posedness and Large Time Behaviour for the Non-cutoff Kac Equation with a Gaussian Thermostat


DOI: 10.1007/s10955-009-9872-4

Cite this article as:
Bagland, V. J Stat Phys (2010) 138: 838. doi:10.1007/s10955-009-9872-4


We consider here a Kac equation with a Gaussian thermostat in the case of a non-cutoff cross section. Under the sole assumptions of finite mass and finite energy for the initial data, we prove the existence of a global in time solution for which mass and energy are preserved. Then, via Fourier transform techniques, we show that this solution is smooth, unique and converges to the corresponding stationary state.

Kac equation without cutoff Thermostat Existence Fourier transform Uniqueness Smoothness Large time behaviour 

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Laboratoire de MathématiquesClermont Université, Université Blaise PascalClermont-FerrandFrance
  2. 2.Laboratoire de MathématiquesCNRS, UMR 6620AubiereFrance

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