Preprints - IAM Publications


	2019 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 Massimiliano Gubinelli, Herbert Koch and Tadahiro Oh Renormalization of the two-dimensional stochastic nonlinear wave equations Transactions of the American Mathematical Society 2018 10.1090/tran/7452

	Massimiliano Gubinelli, Herbert Koch and Tadahiro Oh Paracontrolled approach to the three-dimensional stochastic nonlinear wave equation with quadratic nonlinearity 2018 http://arxiv.org/abs/1811.07808

	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

	Herbert Koch and Xian Liao Conserved energies for the one dimensional Gross-Pitaevskii equation: small energy case 2018 https://arxiv.org/abs/1801.08386

	2017 Herbert Koch and Junfeng Li Global well-posedness and scattering for small data for the three-dimensional Kadomtsev--Petviashvili II equation Communications in Partial Differential Equations, 42(6): 950--976 2017 https://doi.org/10.1080/03605302.2017.1320410

	2016 Patrick Gérard and Herbert Koch The cubic Szegő flow at low regularity Séminaire Laurent SchwartzâÉquations aux dérivées partielles et applications. Année, 2017 2016 http://slsedp.cedram.org/item?id=SLSEDP_2016-2017____A14_0

	Herbert Koch, Angkana Rüland and Wenhui Shi The variable coefficient thin obstacle problem: Carleman inequalities Adv. Math., 301: 820--866 2016 http://dx.doi.org/10.1016/j.aim.2016.06.023

	2015 Tristan Buckmaster and Herbert Koch The Korteweg--de Vries equation at H- 1 regularity Ann. I. H. Poincaré - AN, 32: 1071-1098 2015 http://dx.doi.org/10.1016/j.anihpc.2014.05.004 Abstract: In this paper we will prove the existence of weak solutions to the Korteweg-de Vries initial value problem on the real line with H^-1 initial data; moreover, we will study the problem of orbital and asymptotic H^s stability of solitons for integers s≥ -1; finally, we will also prove new a priori H^-1 bounds for solutions to the Korteweg-de Vries equation. The paper will utilise the Miura transformation to link the Korteweg-de Vries equation to the modified Korteweg-de Vries equation.

	Herbert Koch and Nikolai Nadirashvili Partial analyticity and nodal sets for nonlinear elliptic systems 2015 http://arxiv.org/abs/1506.06224

	Herbert Koch and Stefan Steinerberger Convolution Estimates for Singular Measures and Some Global Nonlinear Brascamp-Lieb Inequalities Proceedings of the Royal Society of Edinburgh, Section: A Mathematics, 145(6): 1223-1237 2015 http://arxiv.org/abs/1404.4536 Abstract: We give an L2 x L2 → L2 convolution estimate for singular measures supported on transversal hypersurfaces in ℝn, which improves earlier results of Bejenaru et al. as well as Bejenaru and Herr. The quantities arising are relevant to the study of the validity of bilinear estimates for dispersive partial differential equations. We also prove a class of global, nonlinear Brascamp–Lieb inequalities with explicit constants in the same spirit.

	Herbert Koch, Angkana Rüland and Wenhui Shi The Variable Coefficient Thin Obstacle Problem: Optimal Regularity and Regularity of the Regular Free Boundary 2015 http://arXiv.org/abs/1504.03525

	Herbert Koch Self-similar solutions to super-critical gKdV Nonlinearity, 28(3): 545-575 2015 http://dx.doi.org/10.1088/0951-7715/28/3/545

	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.

	Herbert Koch and Wolfgang Lück On the spectral density function of the Laplacian of a graph Expo. Math., 32(2): 178-189 2014 http://dx.doi.org/10.1016/j.exmath.2013.09.001 Abstract: Let X be a finite graph. Let \|V\| be the number of its vertices and d be its degree. Denote by F1(X) its first spectral density function which counts the number of eigenvalues ≤λ2 of the associated Laplace operator. We provide an elementary proof for the estimate F1(X)(λ)−F1(X)(0)≤2⋅(\|V\|−1)⋅d⋅λ for 0≤λ<1 which has already been proved by Friedman (1996) [3] before. We explain how this gives evidence for conjectures about approximating Fuglede–Kadison determinants and L2-torsion.

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