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| Autors principals: | , |
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| Format: | Recurso digital |
| Idioma: | |
| Publicat: |
Zenodo
2026
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| Matèries: | |
| Accés en línia: | https://doi.org/10.5281/zenodo.18632006 |
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- 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.