L2-stability of the Landau equation near global Maxwellians

We present an L-2-stability of the kinetic Landau equation for a single species charged plasma with an inverse power-law interaction force in the perturbative regime of global Maxwellians. Our result demonstrates that the L-2-distance between two classical solutions to the Landau equation can be controlled by that between corresponding initial data in a Lipschitz manner. The Coulomb interaction is known to be the singular and marginal case of the theory of the Boltzmann equation where the grazing collisions are the dominant. For some class of classical solutions, we show that our L-2-stability result can provide a uniform L-2-stability. (C) 2015 AIP Publishing LLC.