Damanik, DavidGoldstein, Michael2015-09-242015-09-242015Damanik, 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.https://hdl.handle.net/1911/81709We 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.engThis is an author's peer-reviewed final manuscript, as accepted by the publisher.Journal articlehttp://dx.doi.org/10.1090/jams/837