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Roland Donninger

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Publications associées (20)

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On pointwise decay of linear waves on a Schwarzschild black hole background

Roland Donninger

We prove sharp pointwise

t^{-3}

decay for scalar linear perturbations of a Schwarzschild black hole without symmetry assumptions on the data. We also consider electromagnetic and gravitational perturbations for which we obtain decay rates

t^{-4}

, and $ ...

Springer Verlag2012

A proof of Price's Law on Schwarzschild black hole manifolds for all angular momenta

Roland Donninger

Price's Law states that linear perturbations of a Schwarzschild black hole fall off as

t^{-2\ell-3}

for

t \to \infty

provided the initial data decay sufficiently fast at spatial infinity. Moreover, if the perturbations are initially static (i.e., their ...

2011

Nonlinear Stability of Self-Similar Solutions for Semilinear Wave Equations

Roland Donninger

We prove nonlinear stability of the fundamental self-similar solution of the wave equation with a focusing power nonlinearity tt-=p for [image omitted] in the radial case. The proof is based on a semigroup formulation of the wave equation in similarity coo ...

Taylor & Francis2010

The radial wave operator in similarity coordinates

Roland Donninger

We present a rigorous functional analytic setting to study the radial wave equation in similarity coordinates. As an application we analyze linear stability of the fundamental self-similar solution of the wave equation with a focusing power nonlinearity. T ...

American Institute of Physics2010

Decay Estimates for the One-dimensional Wave Equation with an Inverse Power Potential

Roland Donninger

We study the wave equation on the real line with a potential that falls off like vertical bar x vertical bar(-alpha) for vertical bar x vertical bar -> infinity where 2 < alpha infini ...

Oxford University Press2010

A note on the eigenvalues for equivariant maps of the SU(2) sigma-model

Roland Donninger

We numerically calculate the first few eigenvalues of the perturbations of self-similar solutions of the spherically symmetric co-rotational SU(2) sigma-model on Minkowski space. ...

2010

Asymptotics and analytic modes for the wave equation in similarity coordinates

Roland Donninger

We consider the radial wave equation in similarity coordinates within the semigroup formalism. It is known that the generator of the semigroup exhibits a continuum of eigenvalues and embedded in this continuum there exists a discrete set of eigenvalues wit ...

Springer Verlag2009

Spectral Properties And Linear Stability Of Self-Similar Wave Maps

Roland Donninger

We study co-rotational wave maps from (3 + 1)-Minkowski space to the three-sphere S-3. It is known that there exists a countable family {f(n)} of self-similar solutions. We investigate their stability under linear perturbations by operator theoretic method ...

2009

On the mode stability of a self-similar wave map

Roland Donninger

We study linear perturbations of a self-similar wave map from Minkowski space to the three-sphere which is conjectured to be linearly stable. Considering analytic mode solutions of the evolution equation for the perturbations we prove that there are no rea ...

American Institute of Physics2008

Spectral Properties and Stability of Self-Similar Wave Maps

Roland Donninger

In this thesis the Cauchy problem and in particular the question of singularity formation for co--rotational wave maps from 3+1 Minkowski space to the three--sphere

S^3

is studied. Numerics indicate that self--similar solutions of this model play a cruci ...

University of Vienna2007

On pointwise decay of linear waves on a Schwarzschild black hole background

Roland Donninger

We prove sharp pointwise

t^{-3}

t^{-4}

, and $ ...

Springer Verlag2012

Spectral Properties and Stability of Self-Similar Wave Maps

Roland Donninger

In this thesis the Cauchy problem and in particular the question of singularity formation for co--rotational wave maps from 3+1 Minkowski space to the three--sphere

S^3

is studied. Numerics indicate that self--similar solutions of this model play a cruci ...

University of Vienna2007

A proof of Price's Law on Schwarzschild black hole manifolds for all angular momenta

Roland Donninger

Price's Law states that linear perturbations of a Schwarzschild black hole fall off as

t^{-2\ell-3}

for

t \to \infty

provided the initial data decay sufficiently fast at spatial infinity. Moreover, if the perturbations are initially static (i.e., their ...

2011