2025/07/09 by Lucas Broux, Broux, Lucas, Harprit Singh +2 · 1 citation
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA) #Navier-Stokes equation solutions #Nonlinear Partial Differential Equations #Probability (math.PR)
paper · pdf · doi:10.48550/arxiv.2507.06851
openalex publication_date 2025/07/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this work we prove convergence of renormalised models in the framework of regularity structures [Hai14] for a wide class of variable coefficient singular SPDEs in their full subcritical regimes. In particular, we provide for the first time an extension of the main results of [CH16, HS24, BH23] beyond the translation invariant setting. In the non-translation invariant setting, it is necessary to introduce renormalisation functions rather than renormalisation constants. We show that under a very general assumption, which we prove covers the case of second order parabolic operators, these renormalisation functions can be chosen to be local in the sense that their space-time dependence enters only through a finite order jet of the coefficient field of the differential operator at the given space-time point. Furthermore we show that the models we construct depend continuously on the coefficient field.