5 papers
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…
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…
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…
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…
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…