Advances in Differential Equations

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

Cédric Villani

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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

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

First available in Project Euclid: 25 April 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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


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

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