1 citations · 1 across the 6 of their papers we have counts for
8 papers
The Fermi-Pasta-Ulam system and the Korteweg-de Vries equation: a low-regularity continuum limit
Herbert Koch, Ruoyuan Liu
For the infinite Fermi-Pasta-Ulam (FPU) system, general solutions can be approximated by counter-propagating waves associated with solutions to the Korteweg-de Vries (KdV) equation…
The Korteweg-de Vries limit for the global dynamics of the Toda lattice
Ruoyuan Liu, Herbert Koch
It has been observed that the dynamics of the Toda lattice can be well described by solutions of the Korteweg-de Vries (KdV) equation in the continuum limit. We show that, under th…
Mode stability of blow-up for wave maps in the absence of symmetry
Max Weissenbacher, Herbert Koch, Roland Donninger
The wave maps equation in three spatial dimensions with a spherical target admits an explicit blow-up solution. Numerical studies suggest this solution captures the generic blow-up…
Unbounded Yudovich Solutions of the Euler Equations
Dimitri Cobb, Herbert Koch
In this article, we will study unbounded solutions of the 2D incompressible Euler equations. One of the motivating factors for this is that the usual functional framework for the E…
Almost surely smoothed scattering for cubic NLS
Nicolas Burq, Herbert Koch, Nicola Visciglia +1
We consider cubic NLS in dimensions 2, 3, 4 and we prove that almost surely solutions with randomized initial data at low regularity scatter. Moreover, we establish some smoothing…
The Hele-Shaw semi-flow
Thomas Alazard, Herbert Koch
We prove that the Cauchy problem is well-posed in a strong sense and in a general setting. Our main result is the construction of an abstract semi-flow for the Hele-Shaw problem wi…
Wellposedness for the KdV hierarchy
Friedrich Klaus, Herbert Koch, Baoping Liu
We prove a version of wellposedness for all equations of the KdV hierarchy in . Ingredients are 1) The Miura map which allows to define the Gardner hierarchy through the ge…
Global well-posedness and scattering for small data for the 3-d KP-II Cauchy problem
Herbert Koch, Junfeng Li
We study global well-posedness for the Kadomtsev-Petviashvili II equation in three space dimensions with small initial data. The crucial points are new bilinear estimates and the d…