Publications de Joachim Krieger

Concentration compactness for critical radial wave maps

We consider radially symmetric, energy critical wave maps from (1 + 2)-dimensional Minkowski space into the unit sphere

\mathbf{S}^m

, m≥1, and prove global regularity and scattering for classical smooth data of finite energy. In addition, we establish a ...

2018

On stability of type II blow up for the critical NLW on $\mathbb{R}^{3+1}$

Joachim Krieger

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

\mathbb{R}^{3+1}

constructed in [28], [27] are stable along a co-dimension three manifold of radial data perturbations in a suit ...

2018

Small Data Global Regularity For Half-Wave Maps

Joachim Krieger

We formulate the half-wave maps problem with target S-2 and prove global regularity in sufficiently high spatial dimensions for a class of small critical data in Besov spaces. ...

MATHEMATICAL SCIENCE PUBL2018

Global well-posedness for the Yang-Mills equation in 4+1 dimensions: Small energy

Joachim Krieger, Daniel Tataru

We consider the hyperbolic Yang-Mills equation on the Minkowski space

\reels^{4+1}

. Our main result asserts that this problem is globally well-posed for all initial data whose energy is sufficiently small. This solves a longstanding open problem. ...

Annal Mathematics2017

A Class Of Large Global Solutions For The Wave-Map Equation

Joachim Krieger, Elisabetta Chiodaroli

In this paper we consider the equation for equivariant wave maps from R3+1 to S-3 and we prove global in forward time existence of certain C-infinity-smooth solutions which have infinite critical Sobolev norm (H) overdot(3/4) (R-3) x (H) overdot(1/2) (R-3) ...

2017

Small data global regularity for half-wave maps

Joachim Krieger

We formulate the half-wave maps problem with target

S^2

and prove global regularity in sufficiently high spatial dimensions for a class of small critical data in Besov spaces. ...

2017

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

Joachim Krieger, Roland Donninger

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

Global Well-Posedness For The Maxwell-Klein-Gordon Equation In 4+1 Dimensions: Small Energy

Joachim Krieger, Daniel Tataru

We prove that the critical Maxwell-Klein-Gordon equation on R4+1 is globally well-posed for smooth initial data which are small in the energy norm. This reduces the problem of global regularity for large, smooth initial data to precluding concentration of ...

Duke Univ Press2015

Center-stable manifold of the ground state in the energy space for the critical wave equation

Joachim Krieger

We construct a center-stable manifold of the ground state solitons in the energy space for the critical wave equation without imposing any symmetry, as the dynamical threshold between scattering and blow-up, and also as a collection of solutions which stay ...

Springer Verlag2015

Joachim Krieger

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Concentration compactness for critical radial wave maps

On stability of type II blow up for the critical NLW on $\mathbb{R}^{3+1}$

Small Data Global Regularity For Half-Wave Maps

Global well-posedness for the Yang-Mills equation in 4+1 dimensions: Small energy

A Class Of Large Global Solutions For The Wave-Map Equation

Small data global regularity for half-wave maps

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

Global Well-Posedness For The Maxwell-Klein-Gordon Equation In 4+1 Dimensions: Small Energy

Center-stable manifold of the ground state in the energy space for the critical wave equation

On stability of type II blow up for the critical NLW on $\mathbb{R}^{3+1}$

Concentration compactness for critical radial wave maps

Small Data Global Regularity For Half-Wave Maps

A Class Of Large Global Solutions For The Wave-Map Equation

Small data global regularity for half-wave maps

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

Global well-posedness for the Yang-Mills equation in 4+1 dimensions: Small energy

Center-stable manifold of the ground state in the energy space for the critical wave equation

Global Well-Posedness For The Maxwell-Klein-Gordon Equation In 4+1 Dimensions: Small Energy