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5th International ISAAC Congress
July 25-30, 2005
Department of Mathematics and Informatics, University of Catania
Catania, Sicily, Italy

Organizers
International ISAAC Board, Local organizing committee: F. Nicolosi (chairman), S. Bonafede, V. Cataldo, P. Cianci, G.R. Cirmi, S. D'Asero, G. Fiorito, L. Giusti, S. Leonardi, P.E. Ricci

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Uniqueness and stability of a classical solution to a non cut off Boltzmann eqaution
by
Roland Duduchva
Univ. des Saarlandes, Saarbruecken, Germany
Coauthors: R. Kirsch, S. Rjasanov

Existence of a solution to an initial value problem for a spatially homogeneous Boltzmann equation with non cut off collision kernel in the weighted Lebesgue spaces L\langel 2ñ1(R3) was proved by L. Arkeryd in 1973 for soft and hard potentials -1 < \lb £ 1 and by C. Villani in 1998 for soft and very soft potentials -3 < \lb £ -1. These results are valid if the initial data f0 meets the finite entropy condition f0log f0 Î L1(R3) and f0 Î Lá2 ñ1(R3). Stability and uniqueness of solutions to Boltzmann equation was proved only for cut off case and under stronger constraints on the initial data: G. D Blasio 1974, T. Gustafsson 1986, L. Arkeryd 1988 and B. Wennberg 1994.

We prove uniqueness and stability of a classical solution to the Boltzmann equation with non cut off kernels, soft and hard potentials -2 < \lb £ 1.

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Date received: June 14, 2005

Copyright © 2005 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # carf-37.