Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



The exponential decay of global solutions to the generalized Landau equation near Maxwellians

Author: Hongjun Yu
Journal: Quart. Appl. Math. 64 (2006), 29-39
MSC (2000): Primary 35Q99; Secondary 35A05
DOI: https://doi.org/10.1090/S0033-569X-06-00968-4
Published electronically: January 24, 2006
MathSciNet review: 2211376
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Abstract | References | Similar Articles | Additional Information

Abstract: Global-in-time classical solutions near Maxwellians are constructed for the generalized Landau equation in a periodic box for $ \gamma\geq -2$. The exponential decay of such a solution is also obtained.

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  • 1. Degond P. and Lemou M., Dispersion relations for the linearized Fokker-Planck equation. Arch. Rat. Mech. Anal., 138 (2) (1989), 137-167. MR 1463805 (99f:82051)
  • 2. Desvillettes L. and Villani C., On the spatially homogeneous Landau equation for hard potentials I. Existence, uniqueness and smoothness. Comm. P.D.E. 25(1-2), (2000), 179-259. MR 1737547 (2001c:82065)
  • 3. Desvillettes L. and Villani C., On the spatially homogeneous Landau equation for hard potentials II. H-Theorem and application. Comm. P.D.E. 25(1-2), (2000), 261-298. MR 1737548 (2001c:82066)
  • 4. Glassey R., The Cauchy problem in kinetic theory. SIAM, Philadelphia, PA, 1996. MR 1379589 (97i:82070)
  • 5. Guo Y., The Landau Equation in a periodic box. Comm. Math. Phys., 231 (2002), 391-434. MR 1946444 (2004c:82121)
  • 6. Guo Y., Classical solutions to the Boltzmann equation for molecules with angular cutoff. Arch. Rat. Mech. Anal., 169 (2003), 305-353. MR 2013332 (2004i:82054)
  • 7. Guo Y., The Vlasov-Poisson-Boltzmann system near Maxwellians. Comm. Pure Appl. Math., 55 (2002), 1104-1135. MR 1908664 (2003b:82050)
  • 8. Guo Y., The Vlasov-Maxwell-Boltzmann system near Maxwellians. Invent. Math., 153 (2003), 593-630. MR 2000470 (2004m:82123)
  • 9. Strain R. and Guo Y., Almost exponential decay in kinetic equations. Preprint, 2004.
  • 10. Toscani, G. and Villani C., On the trend to equilibrium for some dissipative systems with slowly increasing a priori bounds. J. Statist. Phys., 98 (5-6) (2000), 1279-1309. MR 1751701 (2001g:82069)
  • 11. Yu, H.J., Global solution of the Vlasov-Poisson-Landau systems near Maxwellians with small amplitude., J. Partial Diff. Eqs. 17 (2)(2004), 173-192. MR 2060788
  • 12. Villani C., On a new class of weak solutions to the spatial homogeneous Boltzmann and Landau equations. Arch. Rat. Mech. Anal., 143 (3) (1998), 237-307. MR 1650006 (99j:82065)
  • 13. Villani C., On the Cauchy problem for Landau equation: Sequential stability, global existence. Adv. Diff. Eq. 1 (5) (1996), 793-816. MR 392006 (97e:82048)
  • 14. Villani C., A survey of mathematical topics in kinetic theory. To appear in Handbook of Fluid Mechanics, S. Friedlander and D. Serre, Eds.

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Additional Information

Hongjun Yu
Affiliation: School of Mathematical Sciences, South China University of Technology, Guangzhou 510640, People’s Republic of China and Academy of Mathematics and Systems Science, CAS, Beijing 100080, People’s Republic of China
Email: yuhj@amss.ac.cn

DOI: https://doi.org/10.1090/S0033-569X-06-00968-4
Keywords: Global classical solution, exponential decay, energy estimates
Received by editor(s): June 18, 2004
Published electronically: January 24, 2006
Article copyright: © Copyright 2006 Brown University

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