Kenig, CarlosNahmod, Andrea2024-04-262024-04-262005-01https://hdl.handle.net/20.500.14394/34882<p>DOI <a href="http://dx.doi.org/10.1088/0951-7715/18/5/007">10.1088/0951-7715/18/5/007</a></p>We show an improved local in time existence and uniqueness result for Schrödinger maps and for the hyperbolic–elliptic nonlinear system proposed by Ishimori in analogy with the two-dimensional classical continuous isotropic Heisenberg spin (2d-CCIHS) chain. The proof uses fairly standard gauge geometric tools and energy estimates in combination with Kenig's version of the Koch–Tzvetkov method, to obtain a priori estimates for classical solutions to certain dispersive equations.Mathematicsarticle