Regularity of solutions for the Boltzmann equation without angular cutoff

Comptes Rendus Mathematique

Volumn 347, Issue 13-14, 2009, Pages 747-752

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

^a Ecole Navale   (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: 67349285957     PISSN: 1631073X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.crma.2009.04.025     Document Type: Article

References (16)

1. Alexandre R. Some solutions of the Boltzmann equation without angular cutoff. J. Statist. Phys. 104 (2001) 327-358
2. Alexandre R. Integral estimates for linear singular operator linked with Boltzmann operator. Part I: Small singularities 0 < ν < 1. Indiana Univ. Math. J. 55 (2006) 1975-2021
3. Alexandre R., Desvillettes L., Villani C., and Wennberg B. Entropy dissipation and long-range interactions. Arch. Ration. Mech. Anal. 152 (2000) 327-355
4. Alexandre R., Morimoto Y., Ukai S., Xu C.-J., and Yang T. Uncertainty principle and kinetic equations. J. Funct. Anal. 255 (2008) 2013-2066
5. R. Alexandre, Y. Morimoto, S. Ukai, C.-J. Xu, T. Yang, Regularizing effect and local existence for non-cutoff Boltzmann equation, preprint, 2008
6. Alexandre R., and Safadi M. Littlewood Paley decomposition and regularity issues in Boltzmann equation homogeneous equations. I. Non-cutoff and Maxwell cases. Math. Models Methods Appl. Sci. 15 (2005) 907-920
7. Boudin L., and Desvillettes L. On the singularities of the global small solutions of the full Boltzmann equation. Monatsh. Math. 131 (2000) 91-108
8. Cercignani C. The Boltzmann Equation and Its Applications. Applied Mathematical Sciences vol. 67 (1988), Springer-Verlag
9. Chen Y. Smoothness of classical solutions to the Vlasov-Poisson-Landau System. Kinetic Related Models 1 3 (2008) 369-386
10. Y. Chen, L. Desvillettes, L. He, Smoothing effects for classical solutions of the full Landau equation, Arch. Ration. Mech. Anal., in press
11. Desvillettes L. About the regularization properties of the non-cut-off Kac equation. Comm. Math. Phys. 168 (1995) 417-440
12. Desvillettes L. Regularization properties of the 2-dimensional non-radially symmetric non-cutoff spatially homogeneous Boltzmann equation for Maxwellian molecules. Trans. Theory Stat. Phys. 26 (1997) 341-357
13. Desvillettes L., and Wennberg B. Smoothness of the solution of the spatially homogeneous Boltzmann equation without cutoff. Comm. Partial Differential Equations 29 (2004) 133-155
14. Huo Z.H., Morimoto Y., Ukai S., and Yang T. Regularity of entropy solutions for spatially homogeneous Boltzmann equation without angular cutoff. Kinetic Related Models 1 (2008) 453-489
15. Ukai S. Local solutions in Gevrey classes to the nonlinear Boltzmann equation without cutoff. Japan J. Appl. Math. 1 1 (1984) 141-156
16. Villani C. A review of mathematical topics in collisional kinetic theory. In: Friedlander S., and Serre D. (Eds). Handbook of Mathematical Fluid Dynamics, vol. I (2002), North-Holland, Amsterdam 71-305