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

Cédric Villani

#### 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.

#### Article information

Source
Adv. Differential Equations, Volume 1, Number 5 (1996), 793-816.

Dates
First available in Project Euclid: 25 April 2013

Mathematical Reviews number (MathSciNet)
MR1392006

Zentralblatt MATH identifier
0856.35020

Subjects
Primary: 82D10: Plasmas
Secondary: 35Q99: None of the above, but in this section

#### Citation

Villani, Cédric. On the Cauchy problem for Landau equation: sequential stability, global existence. Adv. Differential Equations 1 (1996), no. 5, 793--816. https://projecteuclid.org/euclid.ade/1366896020