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dc.contributor.authorJiang, R.
dc.contributor.authorLi, K.
dc.contributor.authorXiao, J.
dc.date.accessioned2019-12-09T09:56:02Z
dc.date.available2019-12-09T09:56:02Z
dc.date.issued2019-11
dc.identifier.issn2050-5094
dc.identifier.urihttp://hdl.handle.net/20.500.11824/1051
dc.description.abstractWe show that, if $b\in L^1(0,T;L^1_{\rm {loc}}(\mathbb R))$ has spatial derivative in the John-Nirenberg space ${\rm{BMO}}(\mathbb R)$, then it generates a unique flow $\phi(t,\cdot)$ which has an $A_\infty(\mathbb R)$ density for each time $t\in [0,T]$. Our condition on the map $b$ is not only optimal but also produces a sharp quantitative estimate for the density. As a killer application we achieve the well-posedness for a Cauchy problem of the transport equation in ${\rm{BMO}}(\mathbb R)$.en_US
dc.description.sponsorshipNational Natural Science Foundation of China (11671039, 11771043, 11922114); Juan de la Cierva - Formaci\'on 2015 FJCI-2015-24547; BCAM Severo Ochoa excellence accreditation SEV-2013-0323; NSERC of Canada (20171864)en_US
dc.formatapplication/pdfen_US
dc.language.isoengen_US
dc.rightsReconocimiento-NoComercial-CompartirIgual 3.0 Españaen_US
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/3.0/es/en_US
dc.titleFlow with $A_\infty(\mathbb R)$ density and transport equation in $\mathrm{BMO}(\mathbb R)$en_US
dc.typeinfo:eu-repo/semantics/articleen_US
dc.relation.publisherversionhttp://doi.org/10.1017/fms.2019.41en_US
dc.relation.projectIDES/1PE/MTM2017-82160-C2-1-Pen_US
dc.relation.projectIDEUS/BERC/BERC.2018-2021en_US
dc.rights.accessRightsinfo:eu-repo/semantics/openAccessen_US
dc.type.hasVersioninfo:eu-repo/semantics/publishedVersionen_US
dc.journal.titleForum of Mathematics, Sigmaen_US


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