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We apply the method of time-dependent rescalings which has been developed by G. Rein and the author to a model kinetic equation, to the Euler equations for a perfect polytropic gas and to a model with friction and heat transfer. We build Lyapunov functionals which are in the case of the fluid models improved versions of the estimates which have been found by J.-Y. Chemin and D. Serre

Time-dependent rescalings and Lyapunov functional for some kinetic and fluid models