21 citations · 48 across the 13 of their papers we have counts for
15 papers · 1 filter
Invariant Gibbs measures for the one-dimensional quintic nonlinear Schrödinger equation in infinite volume
Bjoern Bringmann, Gigliola Staffilani
We prove the invariance of the Gibbs measure for the defocusing quintic nonlinear Schrödinger equation on the real line. This builds on earlier work by Bourgain, who treated the cu…
Global well-posedness of the dynamical sine-Gordon model up to
Bjoern Bringmann, Sky Cao
We prove the global well-posedness of the dynamical sine-Gordon model up to the third threshold, i.e., for parameters . The key novelty in our approach is the introductio…
Global well-posedness of the stochastic Abelian-Higgs equations in two dimensions
Bjoern Bringmann, Sky Cao
We prove the global well-posedness of the stochastic Abelian-Higgs equations in two dimensions. The proof is based on a new covariant approach, which consists of two parts: First,…
Invariant Gibbs measures for -dimensional wave maps into Lie groups
Bjoern Bringmann
We discuss the -dimensional wave maps equation with values in a compact Lie group. The corresponding Gibbs measure is given by a Brownian motion on the Lie group, which play…
Well-posedness of a gauge-covariant wave equation with space-time white noise forcing
Bjoern Bringmann, Igor Rodnianski
We first introduce a new model for a two-dimensional gauge-covariant wave equation with space-time white noise. In our main theorem, we obtain the probabilistic global well-posedne…
On Gibbs measures and topological solitons of exterior equivariant wave maps
Bjoern Bringmann
We consider -equivariant wave maps from the exterior spatial domain into the target . This model has infinitely many topological so…
Invariant Gibbs measures for the three dimensional cubic nonlinear wave equation
Bjoern Bringmann, Yu Deng, Andrea R. Nahmod +1
We prove the invariance of the Gibbs measure under the dynamics of the three-dimensional cubic wave equation, which is also known as the hyperbolic -model. This result is th…
The wave maps equation and Brownian paths
Bjoern Bringmann, Jonas Luhrmann, Gigliola Staffilani
We discuss the -dimensional wave maps equation with values in a compact Riemannian manifold . Motivated by the Gibbs measure problem, we consider Brownian paths…
Invariant Gibbs measures for the three-dimensional wave equation with a Hartree nonlinearity II: Dynamics
Bjoern Bringmann
In this two-paper series, we prove the invariance of the Gibbs measure for a three-dimensional wave equation with a Hartree nonlinearity. The novelty lies in the singularity of the…
Invariant Gibbs measures for the three-dimensional wave equation with a Hartree nonlinearity I: Measures
Bjoern Bringmann
In this two-paper series, we prove the invariance of the Gibbs measure for a three-dimensional wave equation with a Hartree nonlinearity. The main novelty is the singularity of the…
Stable blowup for the focusing energy critical nonlinear wave equation under random perturbations
Bjoern Bringmann
We consider the radial focusing energy critical nonlinear wave equation in three spatial dimensions. We establish the stability of the ODE-blowup under random perturbations below t…
Global well-posedness for the fifth-order KdV equation in
Bjoern Bringmann, Rowan Killip, Monica Visan
We prove global well-posedness of the fifth-order Korteweg-de Vries equation on the real line for initial data in . By comparison, the optimal regularity for we…
Almost sure scattering for the energy critical nonlinear wave equation
Bjoern Bringmann
We study the defocusing energy-critical nonlinear wave equation in four dimensions. Our main result proves the stability of the scattering mechanism under random pertubations of th…
Almost sure local well-posedness for a derivative nonlinear wave equation
Bjoern Bringmann
We study the derivative nonlinear wave equation \( - \partial_{tt} u + Δu = |\nabla u|^2 \) on \( \mathbb{R}^{1+3} \). The deterministic theory is determined by the Lorentz-critica…
Almost sure scattering for the radial energy critical nonlinear wave equation in three dimensions
Bjoern Bringmann
We study the Cauchy problem for the radial energy critical nonlinear wave equation in three dimensions. Our main result proves almost sure scattering for radial initial data below…