Global well-posedness for 2D generalized Parabolic Anderson Model via paracontrolled calculus
Fuente:
arXiv
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866911786410704896 |
|---|---|
| author | Shen, Hao Zhu, Rongchan Zhu, Xiangchan |
| author_facet | Shen, Hao Zhu, Rongchan Zhu, Xiangchan |
| contents | This article revisits the problem of global well-posedness for the generalized parabolic Anderson model on $\mathbb{R}^+\times \mathbb{T}^2$ within the framework of paracontrolled calculus \cite{GIP15}. The model is given by the equation:
\begin{equation*}
(\partial_t-Δ) u=F(u)η
\end{equation*}
where $η\in C^{-1-κ}$ with $1/6>κ>0$, and $F\in C_b^2(\mathbb{R})$. Assume that $η\in C^{-1-κ}$ and can be lifted to enhanced noise, we derive new a priori bounds. The key idea follows from the recent work
\cite{CFW24} by A.Chandra, G.L. Feltes and H.Weber to represent the leading error term as a transport type term, and our techniques encompass the paracontrolled calculus, the maximum principle, and the localization approach (i.e. high-low frequency argument). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_19137 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Global well-posedness for 2D generalized Parabolic Anderson Model via paracontrolled calculus Shen, Hao Zhu, Rongchan Zhu, Xiangchan Analysis of PDEs Probability This article revisits the problem of global well-posedness for the generalized parabolic Anderson model on $\mathbb{R}^+\times \mathbb{T}^2$ within the framework of paracontrolled calculus \cite{GIP15}. The model is given by the equation: \begin{equation*} (\partial_t-Δ) u=F(u)η \end{equation*} where $η\in C^{-1-κ}$ with $1/6>κ>0$, and $F\in C_b^2(\mathbb{R})$. Assume that $η\in C^{-1-κ}$ and can be lifted to enhanced noise, we derive new a priori bounds. The key idea follows from the recent work \cite{CFW24} by A.Chandra, G.L. Feltes and H.Weber to represent the leading error term as a transport type term, and our techniques encompass the paracontrolled calculus, the maximum principle, and the localization approach (i.e. high-low frequency argument). |
| title | Global well-posedness for 2D generalized Parabolic Anderson Model via paracontrolled calculus |
| topic | Analysis of PDEs Probability |
| url | https://arxiv.org/abs/2402.19137 |