Publications by Roland Donninger

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

Stable self-similar blowup in energy supercritical Yang-Mills theory

Roland Donninger

We consider the Cauchy problem for an energy supercritical nonlinear wave equation that arises in -dimensional Yang-Mills theory. A certain self-similar solution of this model is conjectured to act as an attractor for generic large data evolutions. Assumin ...

Springer Verlag2014

Stable blow up dynamics for energy supercritical wave equations

Roland Donninger

We study the semilinear wave equation

\displaystyle \partial _t^2 \psi -\Delta \psi =\vert\psi \vert^{p-1}\psi

for

p > 3

with radial data in three spatial dimensions. There exists an explicit solution which blows up at

t=T>0

given by $\displaystyl ...

American Mathematical Society2014

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

Nondispersive Decay For The Cubic Wave Equation

Roland Donninger

We consider the hyperboloidal initial value problem for the cubic focusing wave equation (-partial derivative(2)(t) + Delta(x))nu(t, x) + nu(t, x)(3) = 0, x is an element of R-3 Without symmetry assumptions, we prove the existence of a codimension-4 Lipsch ...

Mathematical Science Publ2014

Nonscattering solutions and blowup at infinity for the critical wave equation

Joachim Krieger, Roland Donninger

We consider the critical focusing wave equation (−∂2t+Δ)u+u5=0 in R1+3 and prove the existence of energy class solutions which are of the form u(t,x)=tμ2W(tμx)+η(t,x) in the forward lightcone {(t,x)∈R×R3:|x|≤t,t≫1} where W(x)=(1+13|x|2)−12 is the ground st ...

Springer Verlag2013

Semiclassical low energy scattering for one-dimensional Schrödinger operators with exponentially decaying potentials

Roland Donninger

We consider semiclassical Schr"odinger operators on the real line of the form

H(\hbar)=-\hbar^2 \frac{d^2}{dx^2}+V(\cdot;\hbar)

with

\hbar>0

small. The potential

V

is assumed to be smooth, positive and exponentially decaying towards infinity. We e ...

Springer Basel Ag2012

Stable self-similar blow up for energy subcritical wave equations

Roland Donninger

We consider the semilinear wave equation partial derivative(2)(t)psi - Delta psi = vertical bar psi vertical bar(p-1)psi for 1 < p

International Press2012

On stable self-similar blow up for equivariant wave maps: The linearized problem

Roland Donninger

We consider co-rotational wave maps from (3+1) Minkowski space into the three-sphere. This is an energy supercritical model which is known to exhibit finite time blow up via self-similar solutions. The ground state self-similar solution

f_0

is known in c ...

2012

Roland Donninger

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

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

Stable self-similar blowup in energy supercritical Yang-Mills theory

Stable blow up dynamics for energy supercritical wave equations

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

Nondispersive Decay For The Cubic Wave Equation

Nonscattering solutions and blowup at infinity for the critical wave equation

Semiclassical low energy scattering for one-dimensional Schrödinger operators with exponentially decaying potentials

Stable self-similar blow up for energy subcritical wave equations

On stable self-similar blow up for equivariant wave maps: The linearized problem

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

Nonscattering solutions and blowup at infinity for the critical wave equation

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

Stable self-similar blowup in energy supercritical Yang-Mills theory

Stable blow up dynamics for energy supercritical wave equations

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

Semiclassical low energy scattering for one-dimensional Schrödinger operators with exponentially decaying potentials

Stable self-similar blow up for energy subcritical wave equations

On stable self-similar blow up for equivariant wave maps: The linearized problem

Nondispersive Decay For The Cubic Wave Equation