| _version_ | 1866901246364876800 |
|---|---|
| author | Revista, Zen MFC, 10 |
| author_facet | Revista, Zen MFC, 10 |
| contents | This monograph presents a rigorous analysis of singular stochastic partial differential equations (SPDEs) within the framework of paracontrolled distributions, as introduced by Gubinelli, Imkeller, and Perkowski. We address the inherent ill-posedness arising from the distributional nature of the driving noise, specifically space-time white noise in dimensions d 2, which renders non-linear terms analytically undefined due to ultraviolet divergences. By employing Littlewood-Paley theory and Bony's paradifferential calculus, we construct a solution space of paracontrolled distributions that permits the algebraic decoupling of the solution into a rough component, determined explicitly by the noise, and a smoother remainder. We rigorously detail the renormalization procedure required to define the resonant interaction terms, specifically focusing on the dynamic 43 model. We establish local well-posedness results in weighted Besov spaces and provide the necessary commutator estimates to control the renormalization constants. |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18632006 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Renormalization of Singular Stochastic Partial Differential Equations via Paracontrolled Distributions Revista, Zen MFC, 10 Singular SPDEs Paracontrolled Distributions Renormalization Stochastic Quantization Besov Spaces This monograph presents a rigorous analysis of singular stochastic partial differential equations (SPDEs) within the framework of paracontrolled distributions, as introduced by Gubinelli, Imkeller, and Perkowski. We address the inherent ill-posedness arising from the distributional nature of the driving noise, specifically space-time white noise in dimensions d 2, which renders non-linear terms analytically undefined due to ultraviolet divergences. By employing Littlewood-Paley theory and Bony's paradifferential calculus, we construct a solution space of paracontrolled distributions that permits the algebraic decoupling of the solution into a rough component, determined explicitly by the noise, and a smoother remainder. We rigorously detail the renormalization procedure required to define the resonant interaction terms, specifically focusing on the dynamic 43 model. We establish local well-posedness results in weighted Besov spaces and provide the necessary commutator estimates to control the renormalization constants. |
| title | Renormalization of Singular Stochastic Partial Differential Equations via Paracontrolled Distributions |
| topic | Singular SPDEs Paracontrolled Distributions Renormalization Stochastic Quantization Besov Spaces |
| url | https://doi.org/10.5281/zenodo.18632006 |