About L p estimates for the spatially homogeneous Boltzmann equation

Laurent Desvillettes; Clément Mouhot

Annales de l'I.H.P. Analyse non linéaire (2005)

  • Volume: 22, Issue: 2, page 127-142
  • ISSN: 0294-1449

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Desvillettes, Laurent, and Mouhot, Clément. "About ${L}^{p}$ estimates for the spatially homogeneous Boltzmann equation." Annales de l'I.H.P. Analyse non linéaire 22.2 (2005): 127-142. <http://eudml.org/doc/78650>.

@article{Desvillettes2005,
author = {Desvillettes, Laurent, Mouhot, Clément},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {functional inequalities; collision operator},
language = {eng},
number = {2},
pages = {127-142},
publisher = {Elsevier},
title = {About $\{L\}^\{p\}$ estimates for the spatially homogeneous Boltzmann equation},
url = {http://eudml.org/doc/78650},
volume = {22},
year = {2005},
}

TY - JOUR
AU - Desvillettes, Laurent
AU - Mouhot, Clément
TI - About ${L}^{p}$ estimates for the spatially homogeneous Boltzmann equation
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 2005
PB - Elsevier
VL - 22
IS - 2
SP - 127
EP - 142
LA - eng
KW - functional inequalities; collision operator
UR - http://eudml.org/doc/78650
ER -

References

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  1. [1] Alexandre R., Desvillettes L., Villani C., Wennberg B., Entropy dissipation and long range interactions, Arch. Rat. Mech. Anal.152 (2000) 327-355. Zbl0968.76076MR1765272
  2. [2] Alexandre R., Villani C., On the Boltzmann equation for long-range interactions, Comm. Pure Appl. Math.55 (2002) 30-70. Zbl1029.82036MR1857879
  3. [3] Arkeryd L., On the Boltzmann equation, Arch. Rat. Mech. Anal.45 (1972) 1-34. Zbl0245.76059MR339665
  4. [4] Arkeryd L., Intermolecular forces of infinite range and the Boltzmann equation, Arch. Rat. Mech. Anal.77 (1981) 11-21. Zbl0547.76085MR630119
  5. [5] Cercignani C., The Boltzmann Equation and its Applications, Springer, 1988. Zbl0646.76001MR1313028
  6. [6] Desvillettes L., Some applications of the method of moments for the homogeneous Boltzmann and Kac equations, Arch. Rat. Mech. Anal.123 (1993) 387-404. Zbl0784.76081MR1233644
  7. [7] Desvillettes L., Villani C., On the spatially homogeneous Landau equation for hard potentials. Part I: Existence, uniqueness and smoothness, Comm. Partial Differential Equations25 (1/2) (2000) 179-259. Zbl0946.35109MR1737547
  8. [8] L. Desvillettes, B. Wennberg, Smoothness of the solution of the spatially homogeneous Boltzmann equation without cutoff, Comm. Partial Differential Equations, submitted for publication. Zbl1103.82020MR2038147
  9. [9] M. Escobedo, P. Laurençot, S. Mischler, On a kinetic equation for coalescing particles, Prépublication Inria, 2003. Zbl1126.82036MR2048557
  10. [10] Goudon T., On Boltzmann equations and Fokker–Planck asymptotics: influence of grazing collisions, J. Stat. Phys.89 (3–4) (1997) 751-776. Zbl0918.35136MR1484062
  11. [11] Gustafsson T., L p -estimates for the nonlinear spatially homogeneous Boltzmann equation, Arch. Rat. Mech. Anal.92 (1986) 23-57. Zbl0619.76100MR816620
  12. [12] Gustafsson T., Global L p -properties for the spatially homogeneous Boltzmann equation, Arch. Rat. Mech. Anal.103 (1988) 1-38. Zbl0656.76067MR946968
  13. [13] Ikenberry E., Truesdell C., On the pressures and the flux of energy in a gas according to Maxwell's kinetic theory. I, Arch. Rat. Mech. Anal.5 (1956) 1-54. Zbl0070.23504MR75725
  14. [14] Lions P.L., Compactness in Boltzmann's equation via Fourier integral operators and applications. I, II, III, J. Math. Kyoto Univ.34 (1994) 539-584. Zbl0884.35124MR1295942
  15. [15] Lions P.L., Regularity and compactness for Boltzmann collision operators without angular cut-off, C. R. Acad. Sci. Paris Sér. I326 (1) (1998) 37-41. Zbl0920.35114MR1649477
  16. [16] Mischler S., Rodriguez Ricard M., Existence globale pour l'équation de Smoluchowski continue non homogène et comportement asymptotique des solutions, C. R. Acad. Sci. Paris Sér. I336 (2003) 407-412. Zbl1036.35072MR1979355
  17. [17] Mischler S., Wennberg B., On the spatially homogeneous Boltzmann equation, Ann. Inst. H. Poincaré Anal. Non Linéaire16 (4) (1999) 467-501. Zbl0946.35075MR1697562
  18. [18] C. Mouhot, C. Villani, Regularity theory for the homogeneous Boltzmann with angular cut-off, Arch. Rat. Mech. Anal., submitted for publication. Zbl1063.76086
  19. [19] Toscani G., Villani C., On the trend to equilibrium for some dissipative systems with slowly increasing a priori bounds, J. Statist. Phys.98 (2000) 1279-1309. Zbl1034.82032MR1751701
  20. [20] Toscani G., Villani C., Probability metrics and uniqueness of the solution to the Boltzmann equation for a Maxwell gas, J. Statist. Phys.94 (1999) 619-637. Zbl0958.82044MR1675367
  21. [21] Villani C., On a new class of weak solutions for the spatially homogeneous Boltzmann and Landau equations, Arch. Rat. Mech. Anal.143 (1998) 273-307. Zbl0912.45011MR1650006
  22. [22] Villani C., Regularity estimates via the entropy dissipation for the spatially homogeneous Boltzmann equation without cut-off, Rev. Mat. Iberoam.15 (1999) 335-352. Zbl0934.45010MR1715411
  23. [23] Wennberg B., On moments and uniqueness for solutions to the space homogeneous Boltzmann equation, Transport Theory Statist. Phys.23 (1994) 533-539. Zbl0812.76080MR1264851
  24. [24] Wennberg B., Entropy dissipation and moment production for the Boltzmann equation, J. Statist. Phys.86 (5–6) (1997) 1053-1066. Zbl0935.82035MR1450762

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