On the rate of convergence to equilibrium for the homogeneous Landau equation with soft potentials

Alexandre Baranger, 2005, Explicit spectral gap estimates for the linearized Boltzmann and Landau operators with hard potentials, Rev. Mat. Iberoam., 21, 819, 10.4171/RMI/436 Beckner, 2008, Pitt's inequality with sharp convolution estimates, Proc. Am. Math. Soc., 136, 1817 Carrapatoso, 2014, Exponential convergence to equilibrium for the homogeneous Landau equation with hard potentials, Bull. Sci. Math. Degond, 1997, Dispersion relations for the linearized Fokker–Planck equation, Arch. Ration. Mech. Anal., 138, 137, 10.1007/s002050050038 Desvillettes, 2007, Large time behavior for the a priori bounds for the solutions to the spatially homogeneous Boltzmann equation with soft potentials, Asymptot. Anal., 54, 235 Desvillettes, 2000, On the spatially homogeneous Landau equation for hard potentials. I. Existence, uniqueness and smoothness, Commun. Partial Differ. Equ., 25, 179, 10.1080/03605300008821512 Desvillettes, 2000, On the spatially homogeneous Landau equation for hard potentials. II. H-theorem and applications, Commun. Partial Differ. Equ., 25, 261, 10.1080/03605300008821513 Desvillettes, 2004, Smoothness of the solution of the spatially homogeneous Boltzmann equation without cutoff, Commun. Partial Differ. Equ., 29, 133 Fournier, 2009, Well-posedness of the spatially homogeneous Landau equation for soft potentials, J. Funct. Anal., 256, 2542, 10.1016/j.jfa.2008.11.008 Gualdani Guo, 2002, The Landau equation in a periodic box, Commun. Math. Phys., 231, 391, 10.1007/s00220-002-0729-9 He, 2014, Asymptotic analysis of the spatially homogeneous Boltzmann equation: grazing collisions limit, J. Stat. Phys., 155, 151, 10.1007/s10955-014-0932-z S. Mischler, C. Mouhot, Exponential stability of slowly decaying solutions to the kinetic Fokker–Planck equation, in preparation. Mischler, 2009, Stability, convergence to self-similarity and elastic limit for the Boltzmann equation for inelastic hard spheres, Commun. Math. Phys., 288, 431, 10.1007/s00220-009-0773-9 Mouhot, 2006, Explicit coercivity estimates for the linearized Boltzmann and Landau operators, Commun. Partial Differ. Equ., 261, 1321, 10.1080/03605300600635004 Mouhot, 2006, Rate of convergence to equilibrium for the spatially homogeneous Boltzmann equation with hard potentials, Commun. Math. Phys., 261, 629, 10.1007/s00220-005-1455-x Mouhot, 2007, Spectral gap and coercivity estimates for the linearized Boltzmann collision operator without angular cutoff, J. Math. Pures Appl., 87, 515, 10.1016/j.matpur.2007.03.003 Toscani, 2000, On the trend to equilibrium for some dissipative systems with slowly increasing a prior bounds, J. Stat. Phys., 98, 1279, 10.1023/A:1018623930325 Tristani, 2014, Exponential convergence to equilibrium for the homogeneous Boltzmann equation without cut-off, J. Stat. Phys., 157, 474, 10.1007/s10955-014-1066-z Villani, 1998, On a new class of weak solutions to the spatially homogeneous Boltzmann and Landau equations, Arch. Ration. Mech. Anal., 143, 273, 10.1007/s002050050106 Villani, 1998, On the spatially homogeneous Landau equation for Maxwellian molecules, Math. Models Methods Appl. Sci., 8, 957, 10.1142/S0218202598000433 Villani, 2002, A review of mathematical topics in collisional kinetic theory, 71, 10.1016/S1874-5792(02)80004-0 Wu, 2014, Global in time estimates for the spatially homogeneous Landau equation with soft potentials, J. Funct. Anal., 266, 3134, 10.1016/j.jfa.2013.11.005