Around 3D Boltzmann non linear operator without angular cutoff, a new formulation
MAPMO, UMR 6627, Département de Mathématiques,
Université d'Orléans, BP 6759 45067 Orleans Cedex 2, France. (email@example.com)
Revised: 22 September 1999
Revised: 22 October 1999
We propose a new formulation of the 3D Boltzmann non linear operator, without assuming Grad's angular cutoff hypothesis, and for intermolecular laws behaving as 1/rs, with s> 2. It involves natural pseudo differential operators, under a form which is analogous to the Landau operator. It may be used in the study of the associated equations, and more precisely in the non homogeneous framework.
Mathematics Subject Classification: 35D05 / 35D10 / 35K70 / 82B40
Key words: Boltzmann operator / ellipticity / non angular cutoff / pseudo differential operators.
© EDP Sciences, SMAI, 2000