Regularity structures and renormalisation of FitzHugh-Nagumo SPDEs in three space dimensions

Abstract

We prove local existence of solutions for a class of suitably renormalised coupled SPDE-ODE systems driven by space-time white noise, where the space dimension is equal to 2 or 3. This class includes in particular the FitzHugh-Nagumo system describing the evolution of action potentials of a large population of neurons, as well as models with multidimensional gating variables. The proof relies on the theory of regularity structures recently developed by M. Hairer, which is extended to include situations with semigroups that are not regularising in space. We also provide explicit expressions for the renormalisation constants, for a large class of cubic nonlinearities.

51 pages. The extension procedure in Section 4 has been substantially modified. Minor changes in Sections 5 and 6 and in the main result

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Cited by in corpus (4)

• Multiscale analysis for traveling-pulse solutions to the stochastic FitzHugh-Nagumo equations
• Quasi-Ergodicity of Transient Patterns in Stochastic Reaction-Diffusion Equations
• An Additive-Noise Approximation to Keller-Segel-Dean-Kawasaki Dynamics: Local Well-Posedness of Paracontrolled Solutions
• Corrigendum to "Regularity structures and renormalisation of FitzHugh-Nagumo SPDEs in three space dimensions"