Comportement en temps long pour l’équation de Landau
Séminaire Laurent Schwartz — EDP et applications (2017-2018), Talk no. 13, 17 p.

Dans cette note nous présentons les résultats de [CM17], obtenus en collaboration avec S. Mischler, concernant l’existence, l’unicité et la convergence vers l’équilibre pour l’équation de Landau (non homogène en espace) avec potentiel coulombien.

Published online:
DOI: 10.5802/slsedp.117
Carrapatoso, Kleber 1

1 IMAG, Université de Montpellier, CNRS Montpellier France
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     title = {Comportement en temps long pour l{\textquoteright}\'equation de {Landau}},
     journal = {S\'eminaire Laurent Schwartz {\textemdash} EDP et applications},
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     pages = {1--17},
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     url = {http://www.numdam.org/articles/10.5802/slsedp.117/}
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Carrapatoso, Kleber. Comportement en temps long pour l’équation de Landau. Séminaire Laurent Schwartz — EDP et applications (2017-2018), Talk no. 13, 17 p. doi : 10.5802/slsedp.117. http://www.numdam.org/articles/10.5802/slsedp.117/

[BM05] C. Baranger and C. Mouhot. Explicit spectral gap estimates for the linearized Boltzmann and Landau operators with hard potentials. Rev. Mat. Iberoamericana, 21(3) :819–841, 2005. | DOI | MR | Zbl

[CDH17] K. Carrapatoso, L. Desvillettes, and L. He. Estimates for the large time behavior of the Landau equation in the Coulomb case. Arch. Ration. Mech. Anal., 224(2) :381–420, 2017. | DOI | MR | Zbl

[CM17] K. Carrapatoso and S. Mischler. Landau equation for very soft and Coulomb potentials near Maxwellians. Ann. PDE, 3(1) :Art. 1, 65 pp, 2017. | DOI | MR | Zbl

[CTW16] K. Carrapatoso, I. Tristani, and K.-C. Wu. Cauchy problem and exponential stability for the inhomogeneous Landau equation. Arch. Rational Mech. Anal., 221(1) :363–418, 2016. | DOI | MR | Zbl

[Des15] L. Desvillettes. Entropy dissipation estimates for the Landau equation in the Coulomb case and applications. J. Funct. Anal., 269(5) :1359–1403, 2015. | DOI | MR | Zbl

[DL89] R. J. DiPerna and P.-L. Lions. On the Cauchy problem for Boltzmann equations : global existence and weak stability. Ann. of Math. (2), 130(2) :321–366, 1989. | DOI | MR | Zbl

[DL97] P. Degond and M. Lemou. Dispersion relations for the linearized Fokker-Planck equation. Arch. Ration. Mech. Anal., 138 :137–167, 1997. | DOI | MR | Zbl

[DV05] L. Desvillettes and C. Villani. On the trend to global equilibrium for spatially inhomogeneous kinetic systems : the Boltzmann equation. Invent. Math., 159(2) :245–316, 2005. | DOI | MR | Zbl

[GMM17] M. Gualdani, S. Mischler, and C. Mouhot. Factorization for non-symmetric operators and exponential H-Theorem. Mémoires de la SMF, 153 :137 pp, 2017. | DOI

[Guo02] Y. Guo. The Landau equation in a periodic box. Comm. Math. Phys., 231 :391–434, 2002. | DOI | MR | Zbl

[MN06] C. Mouhot and L. Neumann. Quantitative perturbative study of convergence to equilibrium for collisional kinetic models in the torus. Nonlinearity, 19(4) :969–998, 2006. | DOI | MR | Zbl

[Mou06a] C. Mouhot. Explicit coercivity estimates for the linearized Boltzmann and Landau operators. Comm. Part. Diff Equations, 261 :1321–1348, 2006. | DOI | MR | Zbl

[Mou06b] C. Mouhot. Rate of convergence to equilibrium for the spatially homogeneous Boltzmann equation with hard potentials. Comm. Math. Phys., 261 :629–672, 2006. | DOI | MR | Zbl

[MS07] C. Mouhot and R. Strain. Spectral gap and coercivity estimates for the linearized Boltzmann collision operator without angular cutoff. J. Math. Pures Appl., 87 :515–535, 2007. | DOI | MR | Zbl

[SG06] R. M. Strain and Y. Guo. Almost exponential decay near Maxwellian. Comm. Partial Differential Equations, 31(1-3) :417–429, 2006. | DOI | MR | Zbl

[SG08] R. M. Strain and Y. Guo. Exponential decay for soft potentials near Maxwellian. Arch. Ration. Mech. Anal., 187(2) :287–339, 2008. | DOI | MR | Zbl

[Vil96] C. Villani. On the Cauchy problem for Landau equation : sequential stability, global existence. Adv. Differential Equations, 1(5) :793–816, 1996. | Zbl

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