Abstract:
We study a higher order dispersion nonlinear Schr6dinger (NLS) equation with the k-Laplacian (-Δ)k, and the potential term expressed as a power nonlinearity (for any positive power). When k = 1 we recover the NLS with the standard Laplacian and when k = 2 we get the bi-harmonic NLS. We investigate well-posedness of solutions to this higher order NLS equation on a subset of a Sobolev space by constructing a weighted space with polynomial weights. We obtain linear estimates with fractional weights, apply it in the nonlinear setting and conclude the local well-posedness.
Place: Monzón 316
Hour: 3:30 p.m.