Well-posedness for Hardy-H\'enon parabolic equations with fractional Brownian noise

TL;DR

This paper investigates the well-posedness of Hardy-Hénon parabolic equations in low dimensions influenced by fractional Brownian noise, establishing local existence and uniqueness of solutions under specific conditions.

Contribution

It introduces a novel analysis of Hardy-Hénon equations with fractional Brownian noise, proving local well-posedness in certain function spaces.

Findings

Established local existence of solutions

Proved uniqueness under specified conditions

Extended understanding of stochastic PDEs with fractional noise

Abstract

We study the Hardy-H\'enon parabolic equations on $\mathbb{R}^{N}$ ($N=2, 3$) under the effect of an additive fractional Brownian noise with Hurst parameter $H>\max\left(1/2, N/4\right).$ We show local existence and uniqueness of a mid $L^{q}$-solution under suitable assumptions on $q$.