Matches in SemOpenAlex for { <https://semopenalex.org/work/W2733889586> ?p ?o ?g. }
Showing items 1 to 93 of
93
with 100 items per page.
- W2733889586 abstract "We consider the Cauchy problem for the cubic fourth order nonlinear Schrodinger equation (4NLS) on the circle. In particular, we prove global well-posedness of the renormalized 4NLS in negative Sobolev spaces $H^s(mathbb{T})$, $s > -frac{1}{3}$, with enhanced uniqueness. The proof consists of two separate arguments. (i) We first prove global existence in $H^s(mathbb{T})$, $s > -frac{9}{20}$, via the short-time Fourier restriction norm method. By following the argument in Guo-Oh for the cubic NLS, this also leads to non-existence of solutions for the (non-renormalized) 4NLS in negative Sobolev spaces. (ii) We then prove enhanced uniqueness in $H^s(mathbb{T})$, $s > -frac{1}{3}$, by establishing an energy estimate for the difference of two solutions with the same initial condition. For this purpose, we perform an infinite iteration of normal form reductions on the $H^s$-energy functional, allowing us to introduce an infinite sequence of correction terms to the $H^s$-energy functional in the spirit of the $I$-method. In fact, the main novelty of this paper is this reduction of the $H^s$-energy functionals (for a single solution and for the difference of two solutions with the same initial condition) to sums of infinite series of multilinear terms of increasing degrees." @default.
- W2733889586 created "2017-07-14" @default.
- W2733889586 creator A5021896321 @default.
- W2733889586 creator A5090720658 @default.
- W2733889586 date "2017-07-06" @default.
- W2733889586 modified "2023-09-26" @default.
- W2733889586 title "Global well-posedness of the periodic cubic fourth order NLS in negative Sobolev spaces" @default.
- W2733889586 cites W1989559311 @default.
- W2733889586 cites W1991852241 @default.
- W2733889586 cites W2017180326 @default.
- W2733889586 cites W2058165391 @default.
- W2733889586 cites W2075677712 @default.
- W2733889586 cites W2078835008 @default.
- W2733889586 cites W2082676557 @default.
- W2733889586 cites W2118818801 @default.
- W2733889586 cites W2122747502 @default.
- W2733889586 cites W2130044878 @default.
- W2733889586 cites W2183692121 @default.
- W2733889586 cites W2245933989 @default.
- W2733889586 cites W2265697223 @default.
- W2733889586 cites W2464594794 @default.
- W2733889586 cites W2731169828 @default.
- W2733889586 cites W2766052078 @default.
- W2733889586 cites W2962788083 @default.
- W2733889586 cites W2963434671 @default.
- W2733889586 cites W2963807589 @default.
- W2733889586 cites W2964047666 @default.
- W2733889586 cites W2964205306 @default.
- W2733889586 cites W3101649822 @default.
- W2733889586 cites W3175367423 @default.
- W2733889586 doi "https://doi.org/10.48550/arxiv.1707.02013" @default.
- W2733889586 hasPublicationYear "2017" @default.
- W2733889586 type Work @default.
- W2733889586 sameAs 2733889586 @default.
- W2733889586 citedByCount "2" @default.
- W2733889586 countsByYear W27338895862017 @default.
- W2733889586 countsByYear W27338895862023 @default.
- W2733889586 crossrefType "posted-content" @default.
- W2733889586 hasAuthorship W2733889586A5021896321 @default.
- W2733889586 hasAuthorship W2733889586A5090720658 @default.
- W2733889586 hasBestOaLocation W27338895861 @default.
- W2733889586 hasConcept C10138342 @default.
- W2733889586 hasConcept C105795698 @default.
- W2733889586 hasConcept C134306372 @default.
- W2733889586 hasConcept C162324750 @default.
- W2733889586 hasConcept C17744445 @default.
- W2733889586 hasConcept C182306322 @default.
- W2733889586 hasConcept C186370098 @default.
- W2733889586 hasConcept C191795146 @default.
- W2733889586 hasConcept C199539241 @default.
- W2733889586 hasConcept C202444582 @default.
- W2733889586 hasConcept C26955809 @default.
- W2733889586 hasConcept C2777021972 @default.
- W2733889586 hasConcept C33923547 @default.
- W2733889586 hasConcept C37914503 @default.
- W2733889586 hasConcept C84392682 @default.
- W2733889586 hasConcept C99730327 @default.
- W2733889586 hasConceptScore W2733889586C10138342 @default.
- W2733889586 hasConceptScore W2733889586C105795698 @default.
- W2733889586 hasConceptScore W2733889586C134306372 @default.
- W2733889586 hasConceptScore W2733889586C162324750 @default.
- W2733889586 hasConceptScore W2733889586C17744445 @default.
- W2733889586 hasConceptScore W2733889586C182306322 @default.
- W2733889586 hasConceptScore W2733889586C186370098 @default.
- W2733889586 hasConceptScore W2733889586C191795146 @default.
- W2733889586 hasConceptScore W2733889586C199539241 @default.
- W2733889586 hasConceptScore W2733889586C202444582 @default.
- W2733889586 hasConceptScore W2733889586C26955809 @default.
- W2733889586 hasConceptScore W2733889586C2777021972 @default.
- W2733889586 hasConceptScore W2733889586C33923547 @default.
- W2733889586 hasConceptScore W2733889586C37914503 @default.
- W2733889586 hasConceptScore W2733889586C84392682 @default.
- W2733889586 hasConceptScore W2733889586C99730327 @default.
- W2733889586 hasLocation W27338895861 @default.
- W2733889586 hasLocation W27338895862 @default.
- W2733889586 hasLocation W27338895863 @default.
- W2733889586 hasLocation W27338895864 @default.
- W2733889586 hasOpenAccess W2733889586 @default.
- W2733889586 hasPrimaryLocation W27338895861 @default.
- W2733889586 hasRelatedWork W2007779322 @default.
- W2733889586 hasRelatedWork W2087413753 @default.
- W2733889586 hasRelatedWork W2087968352 @default.
- W2733889586 hasRelatedWork W2969576389 @default.
- W2733889586 hasRelatedWork W2992532830 @default.
- W2733889586 hasRelatedWork W3035443327 @default.
- W2733889586 hasRelatedWork W3171839086 @default.
- W2733889586 hasRelatedWork W4206208989 @default.
- W2733889586 hasRelatedWork W4303580676 @default.
- W2733889586 hasRelatedWork W4382469906 @default.
- W2733889586 isParatext "false" @default.
- W2733889586 isRetracted "false" @default.
- W2733889586 magId "2733889586" @default.
- W2733889586 workType "article" @default.