A priori bounds for stochastic porous media equations via regularity structures
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866911044272652288 |
|---|---|
| author | Tempelmayr, Markus Weber, Hendrik |
| author_facet | Tempelmayr, Markus Weber, Hendrik |
| contents | We prove a priori bounds for solutions of singular stochastic porous media equations with multiplicative noise in their natural $L^1$-based regularity class. We consider the first singular regime, i.e.~noise of space-time regularity $α-2$ for $α\in(2/3,1)$, and prove modelledness of the solution in the sense of regularity structures with respect to the solution of the corresponding linear stochastic heat equation. The proof relies on the kinetic formulation of the equation and a novel renormalized energy inequality. A careful analysis allows to balance the degeneracy of the diffusion coefficient against sufficiently strong damping of the multiplicative noise for small values of the solution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_03575 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A priori bounds for stochastic porous media equations via regularity structures Tempelmayr, Markus Weber, Hendrik Analysis of PDEs Probability 60H17, 35K65 We prove a priori bounds for solutions of singular stochastic porous media equations with multiplicative noise in their natural $L^1$-based regularity class. We consider the first singular regime, i.e.~noise of space-time regularity $α-2$ for $α\in(2/3,1)$, and prove modelledness of the solution in the sense of regularity structures with respect to the solution of the corresponding linear stochastic heat equation. The proof relies on the kinetic formulation of the equation and a novel renormalized energy inequality. A careful analysis allows to balance the degeneracy of the diffusion coefficient against sufficiently strong damping of the multiplicative noise for small values of the solution. |
| title | A priori bounds for stochastic porous media equations via regularity structures |
| topic | Analysis of PDEs Probability 60H17, 35K65 |
| url | https://arxiv.org/abs/2507.03575 |