Matches in SemOpenAlex for { <https://semopenalex.org/work/W2897384273> ?p ?o ?g. }
- W2897384273 abstract "In this paper we consider globally defined solutions of Camassa-Holm (CH) type equations outside the well-known nonzero speed, peakon region. These equations include the standard CH and Degasperis-Procesi (DP) equations, as well as nonintegrable generalizations such as the $b$-family, elastic rod and BBM equations. Having globally defined solutions for these models, we introduce the notion of emph{zero-speed and breather solutions}, i.e., solutions that do not decay to zero as $tto +infty$ on compact intervals of space. We prove that, under suitable decay assumptions, such solutions do not exist because the identically zero solution is the global attractor of the dynamics, at least in a spatial interval of size $|x|lesssim t^{1/2-}$ as $tto+infty$. As a consequence, we also show scattering and decay in CH type equations with long range nonlinearities. Our proof relies in the introduction of suitable Virial functionals a la Martel-Merle in the spirit of the works by one of us and Ponce, and Kowalczyk-Martel adapted to CH, DP and BBM type dynamics, one of them placed in $L^1_x$, and a second one in the energy space $H^1_x$. Both functionals combined lead to local in space decay to zero in $|x|lesssim t^{1/2-}$ as $tto+infty$. Our methods do not rely on the integrable character of the equation, applying to other nonintegrable families of CH type equations as well." @default.
- W2897384273 created "2018-10-26" @default.
- W2897384273 creator A5001130262 @default.
- W2897384273 creator A5006963626 @default.
- W2897384273 creator A5055086979 @default.
- W2897384273 creator A5070912455 @default.
- W2897384273 date "2018-10-22" @default.
- W2897384273 modified "2023-09-27" @default.
- W2897384273 title "On the dynamics of zero-speed solutions for Camassa-Holm type equations" @default.
- W2897384273 cites W1492711015 @default.
- W2897384273 cites W1551335708 @default.
- W2897384273 cites W1562293606 @default.
- W2897384273 cites W1658726539 @default.
- W2897384273 cites W1967930895 @default.
- W2897384273 cites W1973025260 @default.
- W2897384273 cites W1973358979 @default.
- W2897384273 cites W1973984954 @default.
- W2897384273 cites W1977607363 @default.
- W2897384273 cites W1979571344 @default.
- W2897384273 cites W1985746984 @default.
- W2897384273 cites W1992001246 @default.
- W2897384273 cites W1996626681 @default.
- W2897384273 cites W1997644782 @default.
- W2897384273 cites W1999466139 @default.
- W2897384273 cites W2002138953 @default.
- W2897384273 cites W2003212506 @default.
- W2897384273 cites W2005380085 @default.
- W2897384273 cites W2006228132 @default.
- W2897384273 cites W2008425231 @default.
- W2897384273 cites W2015363211 @default.
- W2897384273 cites W2026031976 @default.
- W2897384273 cites W2027810635 @default.
- W2897384273 cites W2028497428 @default.
- W2897384273 cites W2041698065 @default.
- W2897384273 cites W2045576051 @default.
- W2897384273 cites W2046765416 @default.
- W2897384273 cites W2064355804 @default.
- W2897384273 cites W2065262579 @default.
- W2897384273 cites W2066458678 @default.
- W2897384273 cites W2067052455 @default.
- W2897384273 cites W2082945961 @default.
- W2897384273 cites W2084217855 @default.
- W2897384273 cites W2087124855 @default.
- W2897384273 cites W2096122980 @default.
- W2897384273 cites W2102961728 @default.
- W2897384273 cites W2122794051 @default.
- W2897384273 cites W2123974695 @default.
- W2897384273 cites W2125919762 @default.
- W2897384273 cites W2133914554 @default.
- W2897384273 cites W2135503370 @default.
- W2897384273 cites W2136437647 @default.
- W2897384273 cites W2140084231 @default.
- W2897384273 cites W2152721261 @default.
- W2897384273 cites W2153847821 @default.
- W2897384273 cites W2160812698 @default.
- W2897384273 cites W2170526996 @default.
- W2897384273 cites W2273174356 @default.
- W2897384273 cites W2521880391 @default.
- W2897384273 cites W2609276960 @default.
- W2897384273 cites W2952886458 @default.
- W2897384273 cites W2953748651 @default.
- W2897384273 cites W2962984647 @default.
- W2897384273 cites W2964094531 @default.
- W2897384273 cites W2964168892 @default.
- W2897384273 cites W2964235313 @default.
- W2897384273 cites W3100203306 @default.
- W2897384273 cites W3103052188 @default.
- W2897384273 cites W3104989625 @default.
- W2897384273 cites W3157902193 @default.
- W2897384273 hasPublicationYear "2018" @default.
- W2897384273 type Work @default.
- W2897384273 sameAs 2897384273 @default.
- W2897384273 citedByCount "1" @default.
- W2897384273 countsByYear W28973842732019 @default.
- W2897384273 crossrefType "posted-content" @default.
- W2897384273 hasAuthorship W2897384273A5001130262 @default.
- W2897384273 hasAuthorship W2897384273A5006963626 @default.
- W2897384273 hasAuthorship W2897384273A5055086979 @default.
- W2897384273 hasAuthorship W2897384273A5070912455 @default.
- W2897384273 hasConcept C121332964 @default.
- W2897384273 hasConcept C134306372 @default.
- W2897384273 hasConcept C138885662 @default.
- W2897384273 hasConcept C145912823 @default.
- W2897384273 hasConcept C155091195 @default.
- W2897384273 hasConcept C164380108 @default.
- W2897384273 hasConcept C186370098 @default.
- W2897384273 hasConcept C18903297 @default.
- W2897384273 hasConcept C189549420 @default.
- W2897384273 hasConcept C200741047 @default.
- W2897384273 hasConcept C24454023 @default.
- W2897384273 hasConcept C24890656 @default.
- W2897384273 hasConcept C2777299769 @default.
- W2897384273 hasConcept C2778572836 @default.
- W2897384273 hasConcept C2780813799 @default.
- W2897384273 hasConcept C33923547 @default.
- W2897384273 hasConcept C37914503 @default.
- W2897384273 hasConcept C41895202 @default.
- W2897384273 hasConcept C62520636 @default.
- W2897384273 hasConcept C86803240 @default.
- W2897384273 hasConcept C98444146 @default.