4 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…
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…