Cauchy problem and exponential stability for the inhomogeneous Landau equation

Abstract

This work deals with the inhomogeneous Landau equation on the torus in the cases of hard, maxwellian and moderately soft potentials. We first investigate the linearized equation and we prove exponential decay estimates for the associated semigroup. We then turn to the nonlinear equation and we use the linearized semigroup decay in order to construct solutions in a close-to-equilibrium setting. Finally, we prove a exponential stability for such a solution, with a rate as close as we want to the optimal rate given by the semigroup decay.

References in corpus (4)

• On the rate of convergence to equilibrium for the homogeneous Landau equation with soft potentials
• Exponential Time Decay Estimates for the Landau Equation on Torus
• Exponential stability of slowly decaying solutions to the kinetic Fokker-Planck equation
• Pointwise Behavior of the Linearized Boltzmann Equation on Torus

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• Non-cutoff Boltzmann equation with soft potentials in the whole space
• A particle method for the homogeneous Landau equation
• Global Existence of Non-cutoff Boltzmann Equation in Weighted Sobolev Space
• Hypoelliptic and spectral estimates for the linearized Landau operator
• A $L^2$ to $L^{\infty }$ approach for the Landau Equation
• The Vlasov-Poisson-Boltzmann/Landau system with polynomial perturbation near Maxwellian
• Analytic smoothing effect for the nonlinear Landau equation of Maxwellian molecules