Roland Donninger | EPFL Graph Search

A vector field method on the distorted Fourier side and decay for wave equations with potentials

We study the Cauchy problem for the one-dimensional wave equation

\partial_t^2 u(t,x)-\partial_x^2 u(t,x)+V(x)u(t,x)=0.

The potential

V

is assumed to be smooth with asymptotic behavior

V(x)\sim -\tfrac14 |x|^{-2}\mbox{ as } |x|\to \infty.

...

2016

Codimension one stability of the catenoid under the vanishing mean curvature flow in Minkowski space

Joachim Krieger, Roland Donninger, Willie Wai Yeung Wong

We study time-like hypersurfaces with vanishing mean curvature in the (3+1) dimensional Minkowski space, which are the hyperbolic counterparts to minimal embeddings of Riemannian manifolds. The catenoid is a stationary solution of the associated Cauchy pro ...

Duke Univ Press2015

Exotic blow up solutions for the $\Box u^5$-focussing wave equation in $\mathbb{R}^3$

Joachim Krieger, Roland Donninger, Min Huang

For the critical focusing wave equation

\Box u = u^5

on

\mathbb{R}^{3+1}

in the radial case, we construct a family of blowup solutions which are obtained from the stationary solutions

W(r)

by means of a dynamical rescaling $\lambda(t)\frac{1}{2}W(\la ...

Michigan Mathematical Journal2014