Well-posedness and large deviations of fractional McKean-Vlasov stochastic reaction-diffusion equations on unbounded domains

TL;DR

This paper establishes the well-posedness and large deviation principles for fractional McKean-Vlasov stochastic reaction-diffusion equations on unbounded domains, advancing understanding of their probabilistic behavior.

Contribution

It proves well-posedness under dissipative conditions and develops a novel approach for large deviations without requiring time Hölder continuity of coefficients.

Findings

Proved well-posedness of the fractional McKean-Vlasov equation.

Established large deviation principles using weak convergence methods.

Achieved results on unbounded domains without compact Sobolev embedding assumptions.

Abstract

This paper is mainly concerned with the large deviation principle of the fractional McKean-Vlasov stochastic reaction-diffusion equation defined on R^n with polynomial drift of any degree. We first prove the well-posedness of the underlying equation under a dissipative condition, and then show the strong convergence of solutions of the corresponding controlled equation with respect to the weak topology of controls, by employing the idea of uniform tail-ends estimates of solutions in order to circumvent the non-compactness of Sobolev embeddings on unbounded domains. We finally establish the large deviation principle of the fractional McKean-Vlasov equation by the weak convergence method without assuming the time Holder continuity of the non-autonomous diffusion coefficients.