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

Authors

    • Laboratoire de MathématiquesClermont Université, Université Blaise Pascal
    • Laboratoire de MathématiquesCNRS, UMR 6620
Article

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

Abstract

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 cutoffThermostatExistenceFourier transformUniquenessSmoothnessLarge time behaviour

Copyright information

© Springer Science+Business Media, LLC 2009