18 papers
A general paracontrolled ansatz for singular SPDEs
Yvain Bruned, Nicolas Moench
We provide a general ansatz for the paracontrolled approach introduced by Gubinelli, Imkeller, Perkowski for treating singular SPDEs. The ansatz proposed covers a large class of eq…
Derivation of resonance-based schemes via normal forms
Yvain Bruned
In this work, we propose a systematic derivation of resonance-based schemes via normal forms. The main idea is to use an arborification map on decorated trees together with a Butch…
Novikov algebras and multi-indices in regularity structures
Yvain Bruned, Vladimir Dotsenko
In this work, we introduce multi-Novikov algebras, a generalisation of Novikov algebras with several binary operations indexed by a given set, and show that the multi-indices recen…
Renormalisation in the flow approach for singular SPDEs
Yvain Bruned, Aurélien Minguella
In this work, we study the renormalisation of singular SPDEs in the flow approach recently developed by Duch. We introduce a general ansatz based on decorated trees for the solutio…
Kruskal-style algorithm for cubic Schrödinger equation molecule reduction
Yvain Bruned, Valentin Clarisse
We are interested in the molecule reduction algorithm introduced by Deng and Hani. They use this algorithm to establish a rigidity theorem, which plays a central role in the kineti…
Cancellations for dispersive PDEs with random initial data
Yvain Bruned, Leonardo Tolomeo
In this work, we provide a combinatorial formalism for dealing with the cancellations that have appeared recently in the context of dispersive PDEs with random initial data. The ma…