Scattering Structure and Landau Damping for Linearized Vlasov Equations with Inhomogeneous Boltzmannian States
We study the linearized Vlasov–Poisson–Ampère equation for non-constant Boltzmannian states with one region of trapped particles in dimension one and construct the eigenstructure in the context of the scattering theory. This is based on the use of semi-discrete variables (moments in velocity), and i...
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| Veröffentlicht in: | Annales Henri Poincaré 2019-08, Vol.20 (8), p.2767-2818 |
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| creator | Després, Bruno |
| description | We study the linearized Vlasov–Poisson–Ampère equation for non-constant Boltzmannian states with one region of trapped particles in dimension one and construct the eigenstructure in the context of the scattering theory. This is based on the use of semi-discrete variables (moments in velocity), and it leads to a new Lippmann–Schwinger variational equation. The continuity in quadratic norm of the operator is proved, and the well posedness is proved for a small value of the scaling parameter. It gives a proof of Linear Landau damping for inhomogeneous Boltzmannian states. The linear HMF model is an example. |
| doi_str_mv | 10.1007/s00023-019-00818-y |
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The linear HMF model is an example.</description><subject>Classical and Quantum Gravitation</subject><subject>Dynamical Systems and Ergodic Theory</subject><subject>Elementary Particles</subject><subject>Landau damping</subject><subject>Linearization</subject><subject>Mathematical and Computational Physics</subject><subject>Mathematical Methods in Physics</subject><subject>Mathematics</subject><subject>Numerical Analysis</subject><subject>Physics</subject><subject>Physics and Astronomy</subject><subject>Quantum Field Theory</subject><subject>Quantum Physics</subject><subject>Relativity Theory</subject><subject>Scattering</subject><subject>Theoretical</subject><subject>Trapped particles</subject><subject>Vlasov equations</subject><issn>1424-0637</issn><issn>1424-0661</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2019</creationdate><recordtype>article</recordtype><recordid>eNp9UctOwzAQjBBIQOEHOFnixCGwtvNojjzKQ4rEgcfVWpx1m6q1i-0Ula8nJQhuXHZXuzOj1UySnHA45wDlRQAAIVPgVQow5uN0s5Mc8ExkKRQF3_2dZbmfHIYwB-BiLKuDxD5pjJF8a6fsKfpOx84TQ9uwui_YsRtcrrZH4zyrW0vo209q2OsCg1uzyXuHsXU2sI82ztiDnbmlm5Il1wV25Rbxc4nWtmh7cYwUjpI9g4tAxz99lLzcTp6v79P68e7h-rJOtazKmArdQC7IlFUujCbQxOFNVxLKIhcoNHJj8qqhxjSSY4YZIQneGN68ZVJXJEfJ2aA7w4Va-XaJfqMctur-slbbXe9WUYhyvOY99nTArrx77yhENXedt_17Sog8y0su86xHiQGlvQvBk_mV5aC2GaghA9VnoL4zUJueJAdSWG0dJv8n_Q_rC8kFjGw</recordid><startdate>20190801</startdate><enddate>20190801</enddate><creator>Després, Bruno</creator><general>Springer International Publishing</general><general>Springer Nature B.V</general><general>Springer Verlag</general><scope>AAYXX</scope><scope>CITATION</scope><scope>1XC</scope><orcidid>https://orcid.org/0000-0002-5954-9407</orcidid></search><sort><creationdate>20190801</creationdate><title>Scattering Structure and Landau Damping for Linearized Vlasov Equations with Inhomogeneous Boltzmannian States</title><author>Després, Bruno</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c397t-2cd052ef7952fce0ce10bc9307652a2ca1ff59dedfd31a4a4eae21df1db43c9e3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2019</creationdate><topic>Classical and Quantum Gravitation</topic><topic>Dynamical Systems and Ergodic Theory</topic><topic>Elementary Particles</topic><topic>Landau damping</topic><topic>Linearization</topic><topic>Mathematical and Computational Physics</topic><topic>Mathematical Methods in Physics</topic><topic>Mathematics</topic><topic>Numerical Analysis</topic><topic>Physics</topic><topic>Physics and Astronomy</topic><topic>Quantum Field Theory</topic><topic>Quantum Physics</topic><topic>Relativity Theory</topic><topic>Scattering</topic><topic>Theoretical</topic><topic>Trapped particles</topic><topic>Vlasov equations</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Després, Bruno</creatorcontrib><collection>CrossRef</collection><collection>Hyper Article en Ligne (HAL)</collection><jtitle>Annales Henri Poincaré</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Després, Bruno</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Scattering Structure and Landau Damping for Linearized Vlasov Equations with Inhomogeneous Boltzmannian States</atitle><jtitle>Annales Henri Poincaré</jtitle><stitle>Ann. 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| source | Springer Nature - Complete Springer Journals |
| subjects | Classical and Quantum Gravitation Dynamical Systems and Ergodic Theory Elementary Particles Landau damping Linearization Mathematical and Computational Physics Mathematical Methods in Physics Mathematics Numerical Analysis Physics Physics and Astronomy Quantum Field Theory Quantum Physics Relativity Theory Scattering Theoretical Trapped particles Vlasov equations |
| title | Scattering Structure and Landau Damping for Linearized Vlasov Equations with Inhomogeneous Boltzmannian States |
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