Existence of local solutions for the Boltzmann equation without angular cutoff

Comptes Rendus Mathematique

Volumn 347, Issue 21-22, 2009, Pages 1237-1242

  Alexandre, Radjesvarane ^a   Morimoto, Yoshinori ^b   Ukai, Seiji ^c   Xu, Chao Jiang ^d   Yang, Tong ^e  

^a French Naval Academy   (France)

^b KYOTO UNIVERSITY   (Japan)

^c Université de Rouen ^*

^d UNIVERSITÉ DE ROUEN   (France)

^e CITY UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 72049095061     PISSN: 1631073X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.crma.2009.09.015     Document Type: Article

References (7)

1. Alexandre R. Some solutions of the Boltzmann equation without angular cutoff. J. Statist. Phys. 104 1-2 (2001) 327-358
2. Alexandre R., Morimoto Y., Ukai S., Xu C.-J., and Yang T. Regularity of solutions for the Boltzmann equation without angular cutoff. C. R. Acad. Sci. Paris, Ser. I 347 13-14 (2009) 747-752
3. R. Alexandre, Y. Morimoto, S. Ukai, C.-J. Xu, T. Yang, Regularizing effect and local existence for non-cutoff Boltzmann equation, preprint, 2009, available via http://hal.archives-ouvertes.fr/hal-00349854/fr/
4. Alexandre R., and Villani C. On the Boltzmann equation for long-range interaction. Comm. Pure Appl. Math. 55 (2002) 30-70
5. Ukai S. Local solutions in Gevrey classes to the nonlinear Boltzmann equation without cutoff. Japan J. Appl. Math. 1 1 (1984) 141-156
6. Villani C. On a new class of weak solutions to the spatially homogeneous Boltzmann and Landau equations. Arch. Ration. Mech. Anal. 143 (1998) 273-307
7. Villani C. A review of mathematical topics in collisional kinetic theory. Handbook of Mathematical Fluid Dynamics, vol. I (2002), North-Holland, Amsterdam 71-305