Corpus ID: 224705306

Probabilistic small data global well-posedness of the energy-critical Maxwell-Klein-Gordon equation.

@article{Krieger2020ProbabilisticSD,
  title={Probabilistic small data global well-posedness of the energy-critical Maxwell-Klein-Gordon equation.},
  author={Joachim Krieger and Jonas Luhrmann and Gigliola Staffilani},
  journal={arXiv: Analysis of PDEs},
  year={2020}
}
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 modified linear-nonlinear decomposition furnished by a delicate "probabilistic" parametrix construction. This is the first global existence result for a geometric wave equation for random initial data at scaling super-critical regularity. 

References

SHOWING 1-10 OF 46 REFERENCES
GLOBAL WELL-POSEDNESS FOR THE MAXWELL-KLEIN GORDON EQUATION IN 4 + 1 DIMENSIONS. SMALL ENERGY.
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 forExpand
ALMOST OPTIMAL LOCAL WELL-POSEDNESS OF THE MAXWELL-KLEIN-GORDON EQUATIONS IN 1 + 4 DIMENSIONS
ABSTRACT We prove that the Maxwell-Klein-Gordon system on relative to the Coulomb gauge is locally well-posed for initial data in for all ϵ > 0. This builds on previous work by Klainerman andExpand
On the almost sure global well-posedness of energy subcritical nonlinear wave equations on R 3
We consider energy sub-critical defocusing nonlinear wave equations on R and establish the existence of unique global solutions almost surely with respect to a unit-scale randomization of the initialExpand
Global Regularity for the Maxwell-Klein-Gordon Equation with Small Critical Sobolev Norm in High Dimensions
Abstract.We show that in dimensions n ≥ 6 one has global regularity for the Maxwell-Klein-Gordon equations in the Coulomb gauge provided that the critical Sobolev norm of the initial data isExpand
Concentration Compactness for the Critical Maxwell-Klein-Gordon Equation
We prove global regularity, scattering and a priori bounds for the energy critical Maxwell-Klein-Gordon equation relative to the Coulomb gauge on $$(1+4)$$(1+4)-dimensional Minkowski space. The proofExpand
Local Well-Posedness of the (4 + 1)-Dimensional Maxwell–Klein–Gordon Equation at Energy Regularity
This paper is the first part of a trilogy [22, 23] dedicated to a proof of global well-posedness and scattering of the $$(4+1)$$(4+1)-dimensional mass-less Maxwell–Klein–Gordon equation (MKG) for anyExpand
Invariant Gibbs measures and global strong solutions for nonlinear Schrödinger equations in dimension two
We consider the defocusing nonlinear Schrodinger equation on $\mathbb{T}^2$ with Wick ordered power nonlinearity, and prove almost sure global well-posedness with respect to the associated GibbsExpand
Random Data Cauchy Theory for Nonlinear Wave Equations of Power-Type on ℝ3
We consider the defocusing nonlinear wave equation of power-type on ℝ3. We establish an almost sure global existence result with respect to a suitable randomization of the initial data. InExpand
Probabilistic global well-posedness of the energy-critical defocusing quintic nonlinear wave equation on ^ 3
  • 2015
We prove almost sure global well-posedness of the energy-critical defocusing quintic nonlinear wave equation on R with random initial data in H(R)×H(R) for s > 1 2 . The main new ingredient is aExpand
Almost-sure scattering for the radial energy-critical nonlinear wave equation in three dimensions
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 the energy space.Expand
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