On the existence and uniqueness of global solutions for the KdV equation with quasi-periodic initial data

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dc.citation.journalTitleJournal of the American Mathematical Society
dc.contributor.authorDamanik, David
dc.contributor.authorGoldstein, Michael
dc.date.accessioned2015-09-24T18:13:00Z
dc.date.available2015-09-24T18:13:00Z
dc.date.issued2015
dc.description.abstractWe consider the KdV equation ∂tu+∂3xu+u∂xu=0 with quasi-periodic initial data whose Fourier coefficients decay exponentially and prove existence and uniqueness, in the class of functions which have an expansion with exponentially decaying Fourier coefficients, of a solution on a small interval of time, the length of which depends on the given data and the frequency vector involved. For a Diophantine frequency vector and for small quasi-periodic data (i.e., when the Fourier coefficients obey |c(m)|≤εexp(−κ0|m|) with ε>0 sufficiently small, depending on κ0>0 and the frequency vector), we prove global existence and uniqueness of the solution. The latter result relies on our recent work [Publ. Math. Inst. Hautes Études Sci. 119 (2014) 217] on the inverse spectral problem for the quasi-periodic Schrӧdinger equation.
dc.identifier.citationDamanik, David and Goldstein, Michael. "On the existence and uniqueness of global solutions for the KdV equation with quasi-periodic initial data." <i>Journal of the American Mathematical Society,</i> (2015) American Mathematical Society: http://dx.doi.org/10.1090/jams/837.
dc.identifier.doihttp://dx.doi.org/10.1090/jams/837
dc.identifier.urihttps://hdl.handle.net/1911/81709
dc.language.isoeng
dc.publisherAmerican Mathematical Society
dc.rightsThis is an author's peer-reviewed final manuscript, as accepted by the publisher.
dc.titleOn the existence and uniqueness of global solutions for the KdV equation with quasi-periodic initial data
dc.typeJournal article
dc.type.dcmiText
dc.type.publicationpost-print
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