dc.contributor.author | Tesfahun, Achenef | |
dc.date.accessioned | 2021-08-04T09:03:20Z | |
dc.date.available | 2021-08-04T09:03:20Z | |
dc.date.created | 2019-03-08T11:16:02Z | |
dc.date.issued | 2020 | |
dc.identifier.issn | 0036-1410 | |
dc.identifier.uri | https://hdl.handle.net/11250/2766131 | |
dc.description.abstract | We prove that the initial value problem for the Dirac equation $(-i\gamma^\mu \partial_\mu + m) \psi= ( \frac{e^{- |x|}}{|x|} \ast ( \overline \psi \psi)) \psi \quad \text{in } \ \mathbb{R}^{1+3}$ is globally well-posed and the solution scatters to free waves asymptotically as $t \rightarrow \pm \infty$ if we start with initial data that are small in $H^s$ for $s>0$. This is an almost critical well-posedness result in the sense that $L^2$ is the critical space for the equation. The main ingredients in the proof are Strichartz estimates, space-time bilinear null-form estimates for free waves in $L^2$, and an application of the $U^p$ and $V^p$ function spaces. | en_US |
dc.language.iso | eng | en_US |
dc.publisher | SIAM | en_US |
dc.title | Small data scattering for a cubic Dirac equation with Hartree type nonlinearity in $\R^{1+3}$ | en_US |
dc.type | Journal article | en_US |
dc.type | Peer reviewed | en_US |
dc.description.version | publishedVersion | en_US |
dc.rights.holder | Copyright 2020 Society for Industrial and Applied Mathematics | en_US |
cristin.ispublished | true | |
cristin.fulltext | original | |
cristin.qualitycode | 2 | |
dc.identifier.doi | 10.1137/17m1155788 | |
dc.identifier.cristin | 1683230 | |
dc.source.journal | SIAM Journal on Mathematical Analysis | en_US |
dc.source.pagenumber | 2969–3003 | en_US |
dc.identifier.citation | SIAM Journal on Mathematical Analysis. 2020, 52(3), 2969–3003 | en_US |
dc.source.volume | 52 | en_US |
dc.source.issue | 3 | en_US |