On the Cauchy problem for Landau equation: sequential stability, global existence

Abstract

We establish here a weak stability result for sequences of solutions of the Landau equation. This result relies on the compactness properties recently shown to hold for the equation, and involves a defect measure. It enables us to prove the global existence of a renormalized solution of the ``Landau equation with a defect measure''. We establish an entropy inequality for this solution, and then study its long-time behavior.