Abstract
The usefulness of NSA in kinetic theory both as a technical and conceptual tool is by now well documented. In the present paper we summarize the picture, concerning NSA methods to prove strong L 1-convergence with time to Maxwellian limits for standard solutions of the Boltzmann equation starting far from equilibrium. As a new result we prove the strong L 1 convergence for the space homogeneous BE without angular cutoff.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Arkeryd, L., Intermolecular forces of infinite range and the Boltzmann equation, Arch. Rat. Mechs. Anal 77 (1981), 11–21.
Arkeryd, L., On the Boltzmann equation in unbounded space far from equilibrium, Comm. Math. Phys. 105 (1986), 205–219.
Arkeryd, L., The nonlinear Boltzmann equation far from equilibrium, in Nonstandard Analysis and its applications, Cambr. UP 1988.
Arkeryd, L., On the strong L 1 trend to equilibrium for the Boltzmann equation, Stud. Appl. Math. 87 (1992), 283–288.
DiPerna, R.J., Lions, P.L., On the Cauchy problem for Boltzmann equations: global existence and weak stability, Ann. Math. 130 (1989), 321–366.
DiPerna, R. J., Lions, P. L., Global solutions of Boltzmann 1 s equation and the entropy inequality, Arch. Rat. Mechs. Anal. 114 (1991), 47–55.
Elmroth, T., Global boundedness of moments of solutions of the Boltzmann equation for forces of infinite range, Arch. Rat. Mechs. Anal. 82 (1983), 1–12.
Gustafsson, T., Global L p properties for the spatially homogeneous Boltzmann eqution, Arch. Rat. Mechs. Anal. 103 (1988), 1–38.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1995 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Arkeryd, L. (1995). Infinite range forces and strong L 1-asymptotics for the space-homogeneous boltzmann equation. In: Albeverio, S.A., Luxemburg, W.A.J., Wolff, M.P.H. (eds) Advances in Analysis, Probability and Mathematical Physics. Mathematics and Its Applications, vol 314. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8451-7_19
Download citation
DOI: https://doi.org/10.1007/978-94-015-8451-7_19
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-4481-5
Online ISBN: 978-94-015-8451-7
eBook Packages: Springer Book Archive