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arXiv · 2011.05907

Algebraic deformation for (S)PDEs

Yvain Bruned·Dominique Manchon
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Abstract

We introduce a new algebraic framework based on the deformation of pre-Lie products. This allows us to provide a new construction of the algebraic objects at play in Regularity Structures in the work arXiv:1610.08468 and in arXiv:2005.01649 for deriving a general scheme for dispersive PDEs at low regularity. This construction also explains how the algebraic structure in arXiv:1610.08468 can be viewed as a deformation of the Butcher-Connes-Kreimer and the extraction-contraction Hopf algebras. We start by deforming various pre-Lie products via a Taylor deformation and then we apply the Guin-Oudom procedure which gives us an associative product whose adjoint can be compared with known coproducts. This work reveals that pre-Lie products and their deformation can be a central object in the study of (S)PDEs.

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BibTeXRIS

Yvain Bruned, Dominique Manchon. 2020-11-11. Algebraic deformation for (S)PDEs. https://doi.org/10.2969/jmsj%2F88028802

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