Large time behavior of the a priori bounds for the solutions to the spatially homogeneous Boltzmann equations with soft potentials

Asymptotic Analysis

Volumn 54, Issue 3-4, 2007, Pages 235-245

  Desvillettes, Laurent ^a   Mouhot, Clément ^b  

^a UNIVERSITÉ PARIS SACLAY   (France)

^b UNIVERSITÉ PARIS DAUPHINE   (France)

Author keywords

Boltzmann equation; Moment bounds; Regularity bounds; Soft potentials; Spatially homogeneous; Uniform in time

Indexed keywords

ASYMPTOTIC ANALYSIS; ENTROPY; POLYNOMIALS; PROBLEM SOLVING;

DISSIPATIVE SYSTEMS; SOFT POTENTIALS; SPATIALLY HOMOGENEOUS; UNIFORM IN TIME;

BOLTZMANN EQUATION;

EID: 35148888786     PISSN: 09217134     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (20)

1. L. Arkeryd, On the Boltzmann equation, Arch. Rational Mech. Anal. 45 (1972), 1-34.
2. A.V Bobylev and C. Cercignani, On the rate of entropy production for the Boltzmann equation, J. Statist. Phys. 94(3-4) (1999), 603-618.
3. C. Cercignani, The Boltzmann Equation and Its Applications, Springer, New York, 1988.
4. C. Cercignani, R. Illner and M. Pulvirenti, The Mathematical Theory of Dilute Gases, Springer, New York, 1994.
5. L. Desvillettes, Some applications of the method of moments for the homogeneous Boltzmann equation, Arch. Rational Mech. Anal. 123 (1993), 387-395.
6. T. Elmroth, Global boundedness of moments of solutions of the Boltzmann equation for forces of infinite range. Arch. Rational Mech. Anal. 82(1) (1983), 1-12.
7. T. Gustafsson, LP -estimates for the nonlinear spatially homogeneous Boltzmann equation, Arch. Rational Mech. Anal. 92(1) (1986), 23-57.
8. P -properties for the spatially homogeneous Boltzmann equation, Arch. Rational Mech, Anal. 103(1) (1988), 1-38.
9. E. Ikenberry and C. Truesdell, On the pressures and the flux of energy in a gas according to Maxwell's kinetic theory. I, J. Rational Mech. Anal. 5 (1956), 1-54.
10. S. Mischler and B. Wennberg, On the spatially homogeneous Boltzmann equation, Ann. Inst. H. Poincaré Anal. Non Linéaire 16 (1999), 467-501.
11. C. Mouhot and C. Villani, Regularity theory for the spatially homogeneous Boltzmann equation with cut-off, Arch. Ratio-nal Mech. Anal. 173 (2004), 169-212.
12. C. Mouhot, Quantitative lower bounds for the full Boltzmann equation, Part I: Periodic boundary conditions, Comm. Partial Diff. Equations 30 (2005), 881-917.
13. G. Toscani and C. Villani, Sharp entropy dissipation bounds and explicit rate of trend to equilibrium for the spatially homogeneous Boltzmann equation, Comm. Math. Phys. 203 (1999), 667-706.
14. G. Toscani and C. Villani, On the trend to equilibrium for some dissipative systems with slowly increasing a priori bounds, J. Statist. Phys. 98 (2000), 1279-1309.
15. C. Villani, Contribution à l'étude mathématique des équations de Boltzmann et de Landau en théorie cinétique des gaz et des plasmas. PhD thesis, Univ. Paris Dauphine, France, 1998.
16. C. Villani, On a new class of weak solutions for the spatially homogeneous Boltzmann and Landau equations, Arch. Rational Mech. Anal. 143 (1998), 273-307.
17. C. Villani, A review of mathematical topics in collisional kinetic theory, in: Handbook of Mathematical Fluid Dynamics, Vol. I, North-Holland, Amsterdam, 2002, pp. 71-305.
18. B. Wennberg, On moments and uniqueness for solutions to the space homogeneous Boltzmann equation, Transport Theory Statist. Phys. 23 (1994), 533-539.
19. B. Wennberg, Entropy dissipation and moment production for the Boltzmann equation, J. Statist. Phys. 86 (1997), 1053-1066.
20. B. Wennberg, Regularity in the Boltzmann equation and the Radon transform, Comm. Partial Diff. Equations 19 (1994), 2057-2074.