Publications by Joachim Krieger

Global controllability and stabilization of the wave Maps equation from a circle to a sphere

Continuing the investigations started in the recent work [12] on semi-global controllability and stabilization of the (1+1)-dimensional wave maps equation with spatial domain

S1

and target

Sk

, where semi-global refers to the

2π

-energy bound, we prov ...

2023

Semi-global controllability of a geometric wave equation

Joachim Krieger, Shengquan Xiang

We prove the semi-global controllability and stabilization of the

(1+1)-

dimensional wave maps equation with spatial domain 𝕊1 and target

𝕊k

. First we show that damping stabilizes the system when the energy is strictly below the threshold

2π

, where ha ...

2022

On the stability of blowup solutions for the critical corotational wave-map problem

Joachim Krieger, Shuang Miao

We show that the finite time blow up solutions for the co-rotational Wave Maps problem constructed in [7,15] are stable under suitably small perturbations within the co-rotational class, provided the scaling parameter

λ(t)=t−1−ν

is sufficiently close to ...

2020

A stability theory beyond the co-rotational setting for critical wave maps blow up

Joachim Krieger, Shuang Miao

We exhibit non-equivariant perturbations of the blowup solutions constructed in [18] for energy critical wave maps into

\mathbb{S}^2

. Our admissible class of perturbations is an open set in some sufficiently smooth topology and vanishes near the light co ...

2020

Probabilistic small data global Well-Posedness of the energy-critical Maxwell-Klein-Gordon equation

Joachim Krieger

We establish probabilistic small data global well-posedness of the energy-critical Maxwell-Klein-Gordon equation relative to the Coulomb gauge for scaling super-critical random initial data. The proof relies on an induction on frequency procedure and a mod ...

2020

Boundary Stabilization of Focusing NLKG near Unstable Equilibria: Radial Case

Joachim Krieger, Shengquan Xiang

We investigate the stability and stabilization of the cubic focusing Klein-Gordon equation around static solutions on the closed ball in

\mathbb{R}^3

. First we show that the system is linearly unstable near the static solution

u\equiv1

for any dissipat ...

2020

Small data global regularity for half-wave maps in n=4 dimensions

Joachim Krieger, Anna Kiesenhofer

We prove that the half-wave maps problem on

\mathbb{R}^{4+1}

with target

S^2

is globally well-posed for smooth initial data which are small in the critical

l^1

based Besov space. This is a formal analogue of the result [17]. ...

2019

Randomization improved Strichartz estimates and global well-posedness for supercritical data

Joachim Krieger

We introduce a novel data randomisation for the free wave equation which leads to the same range of Strichartz estimates as for radial data, albeit in a non-radial context. We then use these estimates to establish global wellposedness for a wave maps type ...

2019

Cost for a controlled linear KdV equation

Joachim Krieger, Shengquan Xiang

The controllability of the linearized KdV equation with right Neumann control is studied in the pioneering work of Rosier [25]. However, the proof is by contradiction arguments and the value of the observability constant remains unknown, though rich mathem ...

2019

Type II solutions Type II blow up solutions with optimal stability properties for the critical focussing nonlinear wave equation on $\R^{3+1}$

Joachim Krieger, Stefano Francesco Burzio

We show that the finite time type II blow up solutions for the energy critical nonlinear wave equation [ \Box u = -u^5 ] on

\R^{3+1}

constructed in \cite{KST}, \cite{KS1} are stable along a co-dimension one Lipschitz manifold of data perturbations in a ...

2018

Joachim Krieger

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Global controllability and stabilization of the wave Maps equation from a circle to a sphere

Semi-global controllability of a geometric wave equation

On the stability of blowup solutions for the critical corotational wave-map problem

A stability theory beyond the co-rotational setting for critical wave maps blow up

Probabilistic small data global Well-Posedness of the energy-critical Maxwell-Klein-Gordon equation

Boundary Stabilization of Focusing NLKG near Unstable Equilibria: Radial Case

Small data global regularity for half-wave maps in n=4 dimensions

Randomization improved Strichartz estimates and global well-posedness for supercritical data

Cost for a controlled linear KdV equation

Type II solutions Type II blow up solutions with optimal stability properties for the critical focussing nonlinear wave equation on $\R^{3+1}$

Type II solutions Type II blow up solutions with optimal stability properties for the critical focussing nonlinear wave equation on $\R^{3+1}$

A stability theory beyond the co-rotational setting for critical wave maps blow up

Cost for a controlled linear KdV equation

On the stability of blowup solutions for the critical corotational wave-map problem

Semi-global controllability of a geometric wave equation

Boundary Stabilization of Focusing NLKG near Unstable Equilibria: Radial Case

Probabilistic small data global Well-Posedness of the energy-critical Maxwell-Klein-Gordon equation

Global controllability and stabilization of the wave Maps equation from a circle to a sphere

Small data global regularity for half-wave maps in n=4 dimensions

Randomization improved Strichartz estimates and global well-posedness for supercritical data