Mihaela Ifrim, Herbert Koch and Daniel Tataru Dispersive decay of small data solutions for the KdV equation 2019 https://arxiv.org/abs/1901.05934
2018
Herbert Koch and Daniel Tataru Conserved energies for the cubic nonlinear Schrödinger equation in one dimension Duke Mathematical Journal, 167(17): 3207â3313 2018 https://arxiv.org/abs/1607.02534
2014
Herbert Koch, Hart F. Smith and Daniel Tataru Sharp $L^p$ bounds on spectral clusters for Lipschitz metrics Amer. J. Math., 136(6): 1629-1663 2014 http://dx.doi.org/10.1353/ajm.2014.0039
Abstract: We establish Lp bounds on L2 normalized spectral clusters for self-adjoint elliptic Dirichlet forms with Lipschitz coefficients. In two dimensions we obtain best possible bounds for all 2 ≤ p ≤ ∞, up to logarithmic losses for 6 < p ≤ 8. In higher dimensions we obtain best possible bounds for a limited range of p.