Existence and Regularity of the Solution of Non homogeneous Schrödinger Equation in Periodic Sobolev Spaces

In this article we prove that the Cauchy problem associated to the Schrödinger equation in periodic Sobolevspaces is well posed. We do this in an intuitive way using Fourier theory and in a fine version using Groupstheory, inspired by works Iorio [3], Santiago and Rojas [12] and [13]. Also, we study the relationshipbetween initial data and differentiability of the solution.Finally, we study the corresponding non-homogeneous problem and prove that it is locally well posed, andthat the solution has continuous dependence with respect to the initial data and the non-homogeneity incompact intervals.