Abstract
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-posedness of this model in the Lorenz gauge. Furthermore, we prove the failure of a probabilistic null-form estimate, which exposes a potential obstruction towards the probabilistic well-posedness of a stochastic Maxwell–Klein–Gordon equation.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 139-193 |
| Number of pages | 55 |
| Journal | Probability and Mathematical Physics |
| Volume | 6 |
| Issue number | 1 |
| DOIs | |
| State | Published - 2025 |
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Atomic and Molecular Physics, and Optics
- Statistical and Nonlinear Physics
Keywords
- Maxwell–Klein–Gordon
- gauge theory
- space-time white noise
- stochastic partial differential equation
- wave equation