{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,9]],"date-time":"2026-01-09T15:30:12Z","timestamp":1767972612894,"version":"3.49.0"},"reference-count":40,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2025,1,8]],"date-time":"2025-01-08T00:00:00Z","timestamp":1736294400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,1,8]],"date-time":"2025-01-08T00:00:00Z","timestamp":1736294400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["11871024"],"award-info":[{"award-number":["11871024"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Nonlinear Sci"],"published-print":{"date-parts":[[2025,2]]},"DOI":"10.1007\/s00332-024-10126-3","type":"journal-article","created":{"date-parts":[[2025,1,8]],"date-time":"2025-01-08T18:55:11Z","timestamp":1736362511000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Landau Damping for Vlasov\u2013Poisson System with Radiation Damping on the Torus"],"prefix":"10.1007","volume":"35","author":[{"given":"Zhaopeng","family":"Wang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xianwen","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2025,1,8]]},"reference":[{"key":"10126_CR1","doi-asserted-by":"publisher","first-page":"296","DOI":"10.1007\/BF01262698","volume":"13","author":"J Batt","year":"1963","unstructured":"Batt, J.: Ein Existenzbeweis f\u00fcr die Vlasov-Gleichung der Stellar-dynamik bei gemittelter Dichte. Arch. Ration. Mech. Anal. 13, 296\u2013308 (1963)","journal-title":"Arch. Ration. Mech. Anal."},{"issue":"3","key":"10126_CR2","doi-asserted-by":"publisher","first-page":"342","DOI":"10.1016\/0022-0396(77)90049-3","volume":"25","author":"J Batt","year":"1977","unstructured":"Batt, J.: Global symmetric solutions of the initial value problem of stellar dynamics. J. Differ. Equ. 25(3), 342\u2013364 (1977)","journal-title":"J. Differ. Equ."},{"issue":"6","key":"10126_CR3","first-page":"411","volume":"313","author":"J Batt","year":"1991","unstructured":"Batt, J., Rein, G.: Global classical solutions of the periodic Vlasov\u2013Poisson system in three dimensions. C. R. Acad. Sci. Paris S\u00e9r. I Math., 313(6), 411\u2013416 (1991)","journal-title":"C. R. Acad. Sci. Paris S\u00e9r. I Math.,"},{"key":"10126_CR4","doi-asserted-by":"crossref","unstructured":"Bauer, S., Kunze, M.: Radiative friction for charges interacting with the radiation field: classical many-particle systems. In: Analysis. Modeling and Simulation of Multiscale Problems, pp. 531\u2013551. Springer, Berlin (2006)","DOI":"10.1007\/3-540-35657-6_19"},{"key":"10126_CR5","doi-asserted-by":"crossref","unstructured":"Bedrossian, J.,\u00a0Masmoudi, N.,\u00a0Mouhot, C.: Landau damping: paraproducts and Gevrey regularity. Ann. PDE, 2(1):Art. 4, 71 (2016)","DOI":"10.1007\/s40818-016-0008-2"},{"issue":"3","key":"10126_CR6","doi-asserted-by":"publisher","first-page":"537","DOI":"10.1002\/cpa.21730","volume":"71","author":"J Bedrossian","year":"2018","unstructured":"Bedrossian, J., Masmoudi, N., Mouhot, C.: Landau damping in finite regularity for unconfined systems with screened interactions. Commun. Pure Appl. Math. 71(3), 537\u2013576 (2018)","journal-title":"Commun. Pure Appl. Math."},{"issue":"4","key":"10126_CR7","doi-asserted-by":"publisher","first-page":"4379","DOI":"10.1137\/20M1386141","volume":"54","author":"J Bedrossian","year":"2022","unstructured":"Bedrossian, J., Masmoudi, N., Mouhot, C.: Linearized wave-damping structure of Vlasov\u2013Poisson in $$\\mathbb{R} ^3$$. SIAM J. Math. Anal. 54(4), 4379\u20134406 (2022)","journal-title":"SIAM J. Math. Anal."},{"issue":"4","key":"10126_CR8","doi-asserted-by":"publisher","first-page":"503","DOI":"10.1016\/s0294-1449(99)80026-2","volume":"16","author":"F Castella","year":"1999","unstructured":"Castella, F.: Propagation of space moments in the Vlasov\u2013Poisson equation and further results. Ann. Inst. H. Poincar\u00e9 Anal. Non Lin\u00e9aire 16(4), 503\u2013533 (1999)","journal-title":"Ann. Inst. H. Poincar\u00e9 Anal. Non Lin\u00e9aire"},{"issue":"5","key":"10126_CR9","doi-asserted-by":"publisher","first-page":"635","DOI":"10.1007\/s10114-016-6310-9","volume":"33","author":"J Chen","year":"2017","unstructured":"Chen, J., Zhang, X.W., Gao, R.: Existence, uniqueness and asymptotic behavior for the Vlasov\u2013Poisson system with radiation damping. Acta Math. Sin. (Engl. Ser.) 33(5), 635\u2013656 (2017)","journal-title":"Acta Math. Sin. (Engl. Ser.)"},{"issue":"2","key":"10126_CR10","doi-asserted-by":"publisher","first-page":"279","DOI":"10.4310\/CMS.2014.v12.n2.a4","volume":"12","author":"Z Chen","year":"2014","unstructured":"Chen, Z., Zhang, X.: Sub-linear estimate of large velocities in a collisionless plasma. Commun. Math. Sci. 12(2), 279\u2013291 (2014)","journal-title":"Commun. Math. Sci."},{"issue":"2","key":"10126_CR11","doi-asserted-by":"publisher","first-page":"435","DOI":"10.1090\/S0002-9947-1986-0825714-8","volume":"294","author":"P Degond","year":"1986","unstructured":"Degond, P.: Spectral theory of the linearized Vlasov\u2013Poisson equation. Trans. Am. Math. Soc. 294(2), 435\u2013453 (1986)","journal-title":"Trans. Am. Math. Soc."},{"key":"10126_CR12","unstructured":"Duan, R., Zhang, Z.: A note on Landau damping of two-species Vlasov\u2013Poisson system. arXiv preprint arXiv:2407.02822 (2024)"},{"key":"10126_CR13","doi-asserted-by":"publisher","first-page":"154","DOI":"10.1016\/j.jde.2023.08.020","volume":"376","author":"A Gagnebin","year":"2023","unstructured":"Gagnebin, A., Iacobelli, M.: Landau damping on the torus for the Vlasov\u2013Poisson system with massless electrons. J. Differ. Equ. 376, 154\u2013203 (2023)","journal-title":"J. Differ. Equ."},{"issue":"4","key":"10126_CR14","doi-asserted-by":"publisher","first-page":"411","DOI":"10.1080\/00411459408203873","volume":"23","author":"R Glassey","year":"1994","unstructured":"Glassey, R., Schaeffer, J.: Time decay for solutions to the linearized Vlasov equation. Transp. Theory Stat. Phys. 23(4), 411\u2013453 (1994)","journal-title":"Transp. Theory Stat. Phys."},{"key":"10126_CR15","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611971477","volume-title":"The Cauchy problem in kinetic theory","author":"RT Glassey","year":"1996","unstructured":"Glassey, R.T.: The Cauchy problem in kinetic theory. Society for Industrial and Applied Mathematics (SIAM), Philadelphia (1996)"},{"issue":"6","key":"10126_CR16","doi-asserted-by":"publisher","first-page":"1679","DOI":"10.4310\/MRL.2021.v28.n6.a3","volume":"28","author":"E Grenier","year":"2021","unstructured":"Grenier, E., Nguyen, T.T., Rodnianski, I.: Landau damping for analytic and Gevrey data. Math. Res. Lett. 28(6), 1679\u20131702 (2021)","journal-title":"Math. Res. Lett."},{"key":"10126_CR17","doi-asserted-by":"crossref","unstructured":"Han-Kwan, D., Nguyen, T.\u00a0T., Rousset, F.: Asymptotic stability of equilibria for screened Vlasov\u2013Poisson systems via pointwise dispersive estimates. Ann. PDE, 7(2):Paper No. 18, 37, (2021)","DOI":"10.1007\/s40818-021-00110-5"},{"issue":"3","key":"10126_CR18","doi-asserted-by":"publisher","first-page":"1405","DOI":"10.1007\/s00220-021-04228-2","volume":"387","author":"D Han-Kwan","year":"2021","unstructured":"Han-Kwan, D., Nguyen, T.T., Rousset, F.: On the linearized Vlasov\u2013Poisson system on the whole space around stable homogeneous equilibria. Commun. Math. Phys. 387(3), 1405\u20131440 (2021)","journal-title":"Commun. Math. Phys."},{"issue":"1","key":"10126_CR19","doi-asserted-by":"publisher","first-page":"19","DOI":"10.1002\/mma.1670040104","volume":"4","author":"E Horst","year":"1982","unstructured":"Horst, E.: On the classical solutions of the initial value problem for the unmodified nonlinear Vlasov equation. II. Special Cases. Math. Methods Appl. Sci. 4(1), 19\u201332 (1982)","journal-title":"Special Cases. Math. Methods Appl. Sci."},{"issue":"2","key":"10126_CR20","doi-asserted-by":"publisher","first-page":"75","DOI":"10.1002\/mma.1670160202","volume":"16","author":"E Horst","year":"1993","unstructured":"Horst, E.: On the asymptotic growth of the solutions of the Vlasov\u2013Poisson system. Math. Methods Appl. Sci. 16(2), 75\u201386 (1993)","journal-title":"Math. Methods Appl. Sci."},{"issue":"17","key":"10126_CR21","doi-asserted-by":"publisher","first-page":"1409","DOI":"10.1002\/(SICI)1099-1476(19961125)19:17<1409::AID-MMA836>3.0.CO;2-2","volume":"19","author":"R Illner","year":"1996","unstructured":"Illner, R., Rein, G.: Time decay of the solutions of the Vlasov\u2013Poisson system in the plasma physical case. Math. Methods Appl. Sci. 19(17), 1409\u20131413 (1996)","journal-title":"Math. Methods Appl. Sci."},{"key":"10126_CR22","doi-asserted-by":"crossref","unstructured":"Ionescu, A.\u00a0D., Pausader, B., Wang, X.,\u00a0Widmayer, K.: Nonlinear Landau damping for the Vlasov\u2013Poisson system in $$\\mathbb{R}^3$$: the Poisson equilibrium. Ann. PDE, 10(1):Paper No. 2, 78 (2024)","DOI":"10.1007\/s40818-023-00161-w"},{"issue":"5","key":"10126_CR23","doi-asserted-by":"publisher","first-page":"857","DOI":"10.1007\/s00023-001-8596-z","volume":"2","author":"M Kunze","year":"2001","unstructured":"Kunze, M., Rendall, A.D.: The Vlasov\u2013Poisson system with radiation damping. Ann. Henri Poincar\u00e9 2(5), 857\u2013886 (2001)","journal-title":"Ann. Henri Poincar\u00e9"},{"key":"10126_CR24","first-page":"574","volume":"16","author":"L Landau","year":"1946","unstructured":"Landau, L.: On the vibrations of the electronic plasma. Akad. Nauk SSSR. Zhurnal Eksper. Teoret. Fiz. 16, 574\u2013586 (1946)","journal-title":"Akad. Nauk SSSR. Zhurnal Eksper. Teoret. Fiz."},{"issue":"2","key":"10126_CR25","doi-asserted-by":"publisher","first-page":"291","DOI":"10.1007\/s00220-011-1246-5","volume":"306","author":"Z Lin","year":"2011","unstructured":"Lin, Z., Zeng, C.: Small BGK waves and nonlinear Landau damping. Commun. Math. Phys. 306(2), 291\u2013331 (2011)","journal-title":"Commun. Math. Phys."},{"issue":"2","key":"10126_CR26","doi-asserted-by":"publisher","first-page":"415","DOI":"10.1007\/BF01232273","volume":"105","author":"P-L Lions","year":"1991","unstructured":"Lions, P.-L., Perthame, B.: Propagation of moments and regularity for the $$3$$-dimensional Vlasov\u2013Poisson system. Invent. Math. 105(2), 415\u2013430 (1991)","journal-title":"Invent. Math."},{"issue":"1","key":"10126_CR27","doi-asserted-by":"publisher","first-page":"68","DOI":"10.1016\/j.matpur.2006.01.005","volume":"86","author":"G Loeper","year":"2006","unstructured":"Loeper, G.: Uniqueness of the solution to the Vlasov\u2013Poisson system with bounded density. J. Math. Pures Appl. (9) 86(1), 68\u201379 (2006)","journal-title":"J. Math. Pures Appl. (9)"},{"issue":"1","key":"10126_CR28","doi-asserted-by":"publisher","first-page":"29","DOI":"10.1007\/s11511-011-0068-9","volume":"207","author":"C Mouhot","year":"2011","unstructured":"Mouhot, C., Villani, C.: On Landau damping. Acta Math. 207(1), 29\u2013201 (2011)","journal-title":"Acta Math."},{"issue":"2","key":"10126_CR29","doi-asserted-by":"publisher","first-page":"549","DOI":"10.3934\/krm.2011.4.549","volume":"4","author":"C Pallard","year":"2011","unstructured":"Pallard, C.: Growth estimates and uniform decay for a collisionless plasma. Kinet. Relat. Models 4(2), 549\u2013567 (2011)","journal-title":"Kinet. Relat. Models"},{"issue":"7","key":"10126_CR30","doi-asserted-by":"publisher","first-page":"803","DOI":"10.1002\/mma.1402","volume":"34","author":"C Pallard","year":"2011","unstructured":"Pallard, C.: A note on the growth of velocities in a collisionless plasma. Math. Methods Appl. Sci. 34(7), 803\u2013806 (2011)","journal-title":"Math. Methods Appl. Sci."},{"issue":"3","key":"10126_CR31","doi-asserted-by":"publisher","first-page":"2864","DOI":"10.1016\/j.jde.2011.09.020","volume":"252","author":"C Pallard","year":"2012","unstructured":"Pallard, C.: Large velocities in a collisionless plasma. J. Differ. Equ. 252(3), 2864\u20132876 (2012)","journal-title":"J. Differ. Equ."},{"issue":"7","key":"10126_CR32","doi-asserted-by":"publisher","first-page":"1273","DOI":"10.1080\/03605302.2011.606863","volume":"37","author":"C Pallard","year":"2012","unstructured":"Pallard, C.: Moment propagation for weak solutions to the Vlasov\u2013Poisson system. Comm. Partial Differ. Equ. 37(7), 1273\u20131285 (2012)","journal-title":"Comm. Partial Differ. Equ."},{"issue":"3","key":"10126_CR33","doi-asserted-by":"publisher","first-page":"1754","DOI":"10.1137\/120881178","volume":"46","author":"C Pallard","year":"2014","unstructured":"Pallard, C.: Space moments of the Vlasov\u2013Poisson system: propagation and regularity. SIAM J. Math. Anal. 46(3), 1754\u20131770 (2014)","journal-title":"SIAM J. Math. Anal."},{"issue":"3\u20134","key":"10126_CR34","first-page":"659","volume":"21","author":"B Perthame","year":"1996","unstructured":"Perthame, B.: Time decay, propagation of low moments and dispersive effects for kinetic equations. Commun. Partial Differ. Equ. 21(3\u20134), 659\u2013686 (1996)","journal-title":"Commun. Partial Differ. Equ."},{"issue":"2","key":"10126_CR35","doi-asserted-by":"publisher","first-page":"281","DOI":"10.1016\/0022-0396(92)90033-J","volume":"95","author":"K Pfaffelmoser","year":"1992","unstructured":"Pfaffelmoser, K.: Global classical solutions of the Vlasov\u2013Poisson system in three dimensions for general initial data. J. Differ. Equ. 95(2), 281\u2013303 (1992)","journal-title":"J. Differ. Equ."},{"key":"10126_CR36","doi-asserted-by":"publisher","first-page":"269","DOI":"10.1002\/mana.19981910114","volume":"191","author":"G Rein","year":"1998","unstructured":"Rein, G.: Growth estimates for the solutions of the Vlasov\u2013Poisson system in the plasma physics case. Math. Nachr. 191, 269\u2013278 (1998)","journal-title":"Math. Nachr."},{"issue":"3","key":"10126_CR37","doi-asserted-by":"publisher","first-page":"262","DOI":"10.1002\/mma.1354","volume":"34","author":"J Schaeffer","year":"2011","unstructured":"Schaeffer, J.: Asymptotic growth bounds for the Vlasov\u2013Poisson system. Math. Methods Appl. Sci. 34(3), 262\u2013277 (2011)","journal-title":"Math. Methods Appl. Sci."},{"issue":"5","key":"10126_CR38","doi-asserted-by":"publisher","first-page":"1183","DOI":"10.3934\/krm.2018046","volume":"11","author":"M Xiao","year":"2018","unstructured":"Xiao, M., Zhang, X.: On global solutions to the Vlasov\u2013Poisson system with radiation damping. Kinet. Relat. Models 11(5), 1183\u20131209 (2018)","journal-title":"Kinet. Relat. Models"},{"key":"10126_CR39","doi-asserted-by":"publisher","first-page":"185","DOI":"10.1007\/s10440-018-0200-3","volume":"160","author":"M Xiao","year":"2019","unstructured":"Xiao, M., Zhang, X.: Moment propagation of the Vlasov\u2013Poisson system with a radiation term. Acta Appl. Math. 160, 185\u2013206 (2019)","journal-title":"Acta Appl. Math."},{"issue":"1","key":"10126_CR40","doi-asserted-by":"publisher","first-page":"548","DOI":"10.1016\/j.jmaa.2007.10.038","volume":"341","author":"X Zhang","year":"2008","unstructured":"Zhang, X., Wei, J.: The Vlasov\u2013Poisson system with infinite kinetic energy and initial data in $$L^p(\\mathbb{R} ^6)$$. J. Math. Anal. Appl. 341(1), 548\u2013558 (2008)","journal-title":"J. Math. Anal. Appl."}],"container-title":["Journal of Nonlinear Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00332-024-10126-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00332-024-10126-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00332-024-10126-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,2,10]],"date-time":"2025-02-10T13:10:23Z","timestamp":1739193023000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00332-024-10126-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,1,8]]},"references-count":40,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2025,2]]}},"alternative-id":["10126"],"URL":"https:\/\/doi.org\/10.1007\/s00332-024-10126-3","relation":{},"ISSN":["0938-8974","1432-1467"],"issn-type":[{"value":"0938-8974","type":"print"},{"value":"1432-1467","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,1,8]]},"assertion":[{"value":"2 December 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"31 December 2024","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"8 January 2025","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"No conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"30"}}