{"title":"关于Landau阻尼中的回声链：行波解和Gevrey 3作为线性稳定阈值","authors":"Christian Zillinger","doi":"10.1007/s40818-020-00090-y","DOIUrl":null,"url":null,"abstract":"<div><p>We show that the linearized Vlasov-Poisson equations around traveling wave-like non-homogeneous states near zero contain the full plasma echo mechanism, yielding Gevrey 3 as a critical stability class. Moreover, here Landau damping may persist despite blow-up: We construct a critical Gevrey regularity class in which the force field converges in <span>\\(L^2\\)</span>. Thus, on the one hand, the physical phenomenon of Landau damping holds. On the other hand, the density diverges to infinity in Sobolev regularity. Hence, “strong damping” cannot hold.</p></div>","PeriodicalId":36382,"journal":{"name":"Annals of Pde","volume":null,"pages":null},"PeriodicalIF":2.4000,"publicationDate":"2021-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s40818-020-00090-y","citationCount":"5","resultStr":"{\"title\":\"On Echo Chains in Landau damping: Traveling Wave-like Solutions and Gevrey 3 as a Linear Stability Threshold\",\"authors\":\"Christian Zillinger\",\"doi\":\"10.1007/s40818-020-00090-y\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We show that the linearized Vlasov-Poisson equations around traveling wave-like non-homogeneous states near zero contain the full plasma echo mechanism, yielding Gevrey 3 as a critical stability class. Moreover, here Landau damping may persist despite blow-up: We construct a critical Gevrey regularity class in which the force field converges in <span>\\\\(L^2\\\\)</span>. Thus, on the one hand, the physical phenomenon of Landau damping holds. On the other hand, the density diverges to infinity in Sobolev regularity. Hence, “strong damping” cannot hold.</p></div>\",\"PeriodicalId\":36382,\"journal\":{\"name\":\"Annals of Pde\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.4000,\"publicationDate\":\"2021-01-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1007/s40818-020-00090-y\",\"citationCount\":\"5\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Annals of Pde\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s40818-020-00090-y\",\"RegionNum\":1,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annals of Pde","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s40818-020-00090-y","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
On Echo Chains in Landau damping: Traveling Wave-like Solutions and Gevrey 3 as a Linear Stability Threshold
We show that the linearized Vlasov-Poisson equations around traveling wave-like non-homogeneous states near zero contain the full plasma echo mechanism, yielding Gevrey 3 as a critical stability class. Moreover, here Landau damping may persist despite blow-up: We construct a critical Gevrey regularity class in which the force field converges in \(L^2\). Thus, on the one hand, the physical phenomenon of Landau damping holds. On the other hand, the density diverges to infinity in Sobolev regularity. Hence, “strong damping” cannot hold.
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