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.

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Cited by in corpus (12)

• Factorization for non-symmetric operators and exponential H-theorem
• The Landau equation with the specular reflection boundary condition
• Regularization estimates and Cauchy theory for inhomogeneous Boltzmann equation for hard potentials without cut-off
• Solving Linearized Landau Equation Pointwisely
• Asymptotics toward viscous contact waves for solutions of the Landau equation
• Non-cutoff Boltzmann equation with soft potentials in the whole space
• Global Existence of Non-cutoff Boltzmann Equation in Weighted Sobolev Space
• A particle method for the homogeneous Landau equation
• A $L^2$ to $L^{\infty }$ approach for the Landau Equation
• Hypoelliptic and spectral estimates for the linearized Landau operator
• Analytic smoothing effect for the nonlinear Landau equation of Maxwellian molecules
• The Vlasov-Poisson-Boltzmann/Landau system with polynomial perturbation near Maxwellian