The Cauchy problem for the Hyperbolic-Elliptic Ishimori system

speaker: Andrea Nahmod (University of Massachusetts at Amherst)

abstract: We show an improved existence result for the hyperbolic-elliptic nonlinear dispersive system proposed by Ishimori in analogy with the 2d CCIHS chain. The proof uses gauge geometric tools and energy estimates in combination with a new method devised by C. Kenig to obtain a priori L^q_t L^{\infty}_x estimates for classical solutions to certain dispersive equations.

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