A priori bounds for quasi-linear SPDEs in the full sub-critical regime
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
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2021
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| _version_ | 1866929289852616704 |
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| author | Otto, Felix Sauer, Jonas Smith, Scott Weber, Hendrik |
| author_facet | Otto, Felix Sauer, Jonas Smith, Scott Weber, Hendrik |
| contents | This paper is concerned with quasi-linear parabolic equations driven by an additive forcing $ξ\in C^{α-2}$, in the full sub-critical regime $α\in (0,1)$. We are inspired by Hairer's regularity structures, however we work with a more parsimonious model indexed by multi-indices rather than trees. This allows us to capture additional symmetries which play a crucial role in our analysis. Assuming bounds on this model, which is modified in agreement with the concept of algebraic renormalization, we prove local a priori estimates on solutions to the quasi-linear equations modified by the corresponding counter terms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2103_11039 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | A priori bounds for quasi-linear SPDEs in the full sub-critical regime Otto, Felix Sauer, Jonas Smith, Scott Weber, Hendrik Analysis of PDEs Probability This paper is concerned with quasi-linear parabolic equations driven by an additive forcing $ξ\in C^{α-2}$, in the full sub-critical regime $α\in (0,1)$. We are inspired by Hairer's regularity structures, however we work with a more parsimonious model indexed by multi-indices rather than trees. This allows us to capture additional symmetries which play a crucial role in our analysis. Assuming bounds on this model, which is modified in agreement with the concept of algebraic renormalization, we prove local a priori estimates on solutions to the quasi-linear equations modified by the corresponding counter terms. |
| title | A priori bounds for quasi-linear SPDEs in the full sub-critical regime |
| topic | Analysis of PDEs Probability |
| url | https://arxiv.org/abs/2103.11039 |