Linear Landau damping in ℝ 3
[Amortissement Landau linéaire en ℝ 3 ]
Toan T. Nguyen1
1 Penn State University Department of Mathematics State College, PA 16802 USA
Journées équations aux dérivées partielles (2023), Exposé no. 8, 14 p.

This article gives an overview on linear Landau damping for collisionless kinetic models such as the non-relativistic Vlasov–Poisson and relativistic Vlasov–Maxwell systems near spatially homogenous radial steady states on the phase space ℝ x 3 ×ℝ v 3 .

Cet article donne un aperçu de l’amortissement Landau linéaire pour les modèles cinétiques sans collision tels que les systèmes non relativistes de Vlasov–Poisson et relativistes de Vlasov–Maxwell proches d’états stationnaires radiaux spatialement homogènes sur l’espace des phases ℝ x 3 ×ℝ v 3 .

Publié le :
DOI : 10.5802/jedp.679
Classification : 35Q83, 35Q61
Keywords: Vlasov–Poisson, Vlasov–Maxwell, Landau damping, Plasma oscillations, Survival threshold

Toan T. Nguyen 1

1 Penn State University Department of Mathematics State College, PA 16802 USA 
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Toan T. Nguyen. Linear Landau damping in $\mathbb{R}^3$. Journées équations aux dérivées partielles (2023), Exposé no. 8, 14 p. doi : 10.5802/jedp.679. https://proceedings.centre-mersenne.org/articles/10.5802/jedp.679/

[1] Claude Bardos; Pierre Degond Global existence for the Vlasov–Poisson equation in 3 space variables with small initial data, Ann. Inst. Henri Poincaré, Anal. Non Linéaire, Volume 2 (1985), pp. 101-118 | DOI | Numdam | MR | Zbl

[2] Claude Bardos; Ha Tien Ngoan; Pierre Degond Existence globale des solutions des équations de Vlasov–Poisson relativistes en dimension 3. (Global solutions for relativistic Vlasov- Poisson equations in three space variables), C. R. Math. Acad. Sci. Paris, Volume 301 (1985), pp. 265-268 | Zbl

[3] Jacob Bedrossian Suppression of plasma echoes and Landau damping in Sobolev spaces by weak collisions in a Vlasov–Fokker–Planck equation, Ann. PDE, Volume 3 (2017) no. 2, 19, 66 pages | DOI | MR | Zbl

[4] Jacob Bedrossian; Nader Masmoudi; Clément Mouhot Landau damping: paraproducts and Gevrey regularity, Ann. PDE, Volume 2 (2016) no. 1, 4, 71 pages | DOI | MR | Zbl

[5] Jacob Bedrossian; Nader Masmoudi; Clément Mouhot Landau damping in finite regularity for unconfined systems with screened interactions, Commun. Pure Appl. Math., Volume 71 (2018) no. 3, pp. 537-576 | DOI | MR | Zbl

[6] Jacob Bedrossian; Nader Masmoudi; Clément Mouhot Linearized wave-damping structure of Vlasov–Poisson in ℝ 3 , SIAM J. Math. Anal., Volume 54 (2022) no. 4, pp. 4379-4406 | DOI | MR | Zbl

[7] Jacob Bedrossian; Fei Wang The linearized Vlasov and Vlasov–Fokker–Planck equations in a uniform magnetic field, J. Stat. Phys., Volume 178 (2020) no. 2, pp. 552-594 | DOI | MR | Zbl

[8] Ira B. Bernstein Waves in a plasma in a magnetic field, Phys. Rev., Volume 109 (1958) no. 1, p. 10 | DOI | Zbl

[9] Léo Bigorgne Sharp asymptotic behavior of solutions of the 3d Vlasov–Maxwell system with small data, Commun. Math. Phys., Volume 376 (2020) no. 2, pp. 893-992 | DOI | MR | Zbl

[10] Léo Bigorgne Global existence and modified scattering for the small data solutions to the Vlasov–Maxwell system (2022) | arXiv

[11] Frédérique Charles; Bruno Després; Alexandre Rege; Ricardo Weder The magnetized Vlasov–Ampère system and the Bernstein–Landau paradox, J. Stat. Phys., Volume 183 (2021) no. 2, 23, 57 pages | DOI | MR | Zbl

[12] Sanchit Chaturvedi; Jonathan Luk; Toan T. Nguyen The Vlasov–Poisson–Landau system in the weakly collisional regime, J. Am. Math. Soc., Volume 36 (2023) no. 4, pp. 1103-1189 | DOI | MR | Zbl

[13] Robert T. Glassey; Jack Schaeffer On time decay rates in Landau damping, Commun. Partial Differ. Equations, Volume 20 (1995) no. 3-4, pp. 647-676 | DOI | MR | Zbl

[14] Robert T. Glassey; Jack W. Schaeffer Global existence for the relativistic Vlasov–Maxwell system with nearly neutral initial data, Commun. Math. Phys., Volume 119 (1988) no. 3, pp. 353-384 | DOI | MR | Zbl

[15] Robert T. Glassey; Jack W. Schaeffer Time decay for solutions to the linearized Vlasov equation, Transp. Theory Stat. Phys., Volume 23 (1994) no. 4, pp. 411-453 | DOI | MR | Zbl

[16] Robert T. Glassey; Walter A. Strauss Absence of shocks in an initially dilute collisionless plasma, Commun. Math. Phys., Volume 113 (1987), pp. 191-208 | DOI | MR | Zbl

[17] Emmanuel Grenier; Toan T. Nguyen; Igor Rodnianski Landau damping for analytic and Gevrey data, Math. Res. Lett., Volume 28 (2021) no. 6, pp. 1679-1702 | DOI | MR | Zbl

[18] Emmanuel Grenier; Toan T. Nguyen; Igor Rodnianski Plasma echoes near stable Penrose data, SIAM J. Math. Anal., Volume 54 (2022) no. 1, pp. 940-953 | DOI | MR | Zbl

[19] Daniel Han-Kwan; Toan T. Nguyen; Frédéric Rousset Long time estimates for the Vlasov–Maxwell system in the non-relativistic limit, Commun. Math. Phys., Volume 363 (2018) no. 2, pp. 389-434 | DOI | MR | Zbl

[20] Daniel Han-Kwan; Toan T. Nguyen; Frédéric Rousset Asymptotic stability of equilibria for screened Vlasov–Poisson systems via pointwise dispersive estimates, Ann. PDE, Volume 7 (2021) no. 2, 18, 37 pages | DOI | MR | Zbl

[21] Daniel Han-Kwan; Toan T. Nguyen; Frédéric Rousset On the linearized Vlasov–Poisson system on the whole space around stable homogeneous equilibria, Commun. Math. Phys., Volume 387 (2021) no. 3, pp. 1405-1440 | DOI | MR | Zbl

[22] Daniel Han-Kwan; Toan T. Nguyen; Frédéric Rousset Linear Landau damping for the Vlasov–Maxwell system in ℝ 3 (2024) | arXiv

[23] Lingjia Huang; Quoc-Hung Nguyen; Yiran Xu Nonlinear Landau damping for the 2d Vlasov–Poisson system with massless electrons around Penrose-stable equilibria (2022) | arXiv

[24] Lingjia Huang; Quoc-Hung Nguyen; Yiran Xu Sharp estimates for screened Vlasov–Poisson system around Penrose-stable equilibria in ℝ d , d≥3 (2022) | arXiv

[25] Alexandru Ionescu; Benoit Pausader; Xuecheng Wang; Klaus Widmayer Nonlinear Landau damping for the Vlasov–Poisson system in ℝ 3 : the Poisson equilibrium (2022) | arXiv

[26] Lev Landau On the vibrations of the electronic plasma. (Russian), Zh. Ehksper. Teor. Fiz., Volume 16 (1946), pp. 574-586

[27] Zhiwu Lin; Walter A. Strauss Nonlinear stability and instability of relativistic Vlasov–Maxwell systems, Commun. Pure Appl. Math., Volume 60 (2007) no. 6, pp. 789-837 | DOI | MR | Zbl

[28] Zhiwu Lin; Walter A. Strauss A sharp stability criterion for the Vlasov–Maxwell system, Invent. Math., Volume 173 (2008) no. 3, pp. 497-546 | DOI | MR | Zbl

[29] Clément Mouhot; Cédric Villani On Landau damping, Acta Math., Volume 207 (2011) no. 1, pp. 29-201 | DOI | MR | Zbl

[30] Toan T. Nguyen Landau damping and the survival threshold (2023) | arXiv

[31] Toan T. Nguyen; Chanjin You Plasmons for the Hartree equations with Coulomb interaction (2023) | arXiv

[32] Isabelle Tristani Landau damping for the linearized Vlasov Poisson equation in a weakly collisional regime, J. Stat. Phys., Volume 169 (2017) no. 1, pp. 107-125 | DOI | MR | Zbl

[33] A. W. Trivelpiece; N. A. Krall Principles of Plasma Physics, McGraw-Hill, 1973

[34] Brent Young On linear Landau damping for relativistic plasmas via Gevrey regularity, J. Differ. Equations, Volume 259 (2015) no. 7, pp. 3233-3273 | DOI | MR | Zbl

[35] Brent Young Landau damping in relativistic plasmas, J. Math. Phys., Volume 57 (2016) no. 2, 021502, 68 pages | DOI | MR | Zbl

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