On the Spatially Homogeneous Landau Equation for Hard Potentials Part Ii : H-theorem and Applications
نویسنده
چکیده
We nd a lower bound for the entropy dissipation of the spatially homogeneous Landau equation with hard potentials in terms of the entropy itself. We deduce from this explicit estimates on the speed of convergence towards equilibrium for the solution of this equation. In the case of so-called overmaxwellian potentials, the convergence is exponential. We also compute a lower bound for the spectral gap of the associated linear operator in this setting. Contents 1. Introduction and main result 1 2. Entropy dissipation : rst method 8 3. Entropy dissipation : second method 13 4. The trend towards equilibrium : overmaxwellian case 15 5. Improved results 18 6. The trend towards equilibrium : the case of true hard potentials 20 7. Poincar e-type inequalities and applications 23 8. Entropy dissipation and regularity estimates 25 Appendix A. Deenition of the entropy dissipation 26 Appendix B. Approximation of the entropy dissipation 28 References 29
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