Journal of Statistical Physics

, Volume 138, Issue 4, pp 838-875

First online:

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

  • Véronique BaglandAffiliated withLaboratoire de Mathématiques, Clermont Université, Université Blaise PascalLaboratoire de Mathématiques, CNRS, UMR 6620 Email author 

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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