Hypoelliptic and spectral estimates for the linearized Landau operator

Abstract

We are interested in the inhomogeneous Landau equation which describes the evolution of a particle density f = f (t, x, v) representing at time t $\ge$ 0, the density of particles at position x $\in$ R 3 and velocity v $\in$ R 3. The study is motivated by the linearization of the Landau equation near Maxwellian distribution. In this article, we establish hypoelliptic estimates, a localization of the spectrum and estimates of the resolvent of the linear Landau operator with hard potentials and Maxwellian molecules. The proof is based on a multiplier method and requires fine pseudo-differential calculus tools.

arXiv admin note: text overlap with arXiv:1003.3265 by other authors

References in corpus (2)

• Cauchy problem and exponential stability for the inhomogeneous Landau equation
• Regularization estimates and Cauchy theory for inhomogeneous Boltzmann equation for hard potentials without cut-off