Liu, YarongWang, YejuanCaraballo Garrido, Tomás2022-09-302022-09-302021-09Liu, Y., Wang, Y. y Caraballo Garrido, T. (2021). The continuity, regularity and polynomial stability of mild solutions for stochastic 2D-Stokes equations with unbounded delay driven by tempered fractional Gaussian noise. Stochastics and Dynamics, 22, 2250022-1-2250022-46.0219-49371793-6799https://hdl.handle.net/11441/137514We consider stochastic 2D-Stokes equations with unbounded delay in fractional power spaces and moments of order p ≥ 2 driven by a tempered fractional Brownian motion (TFBM) Bσ,λ(t) with −1/2 < σ < 0 and λ > 0. First, the global existence and unique ness of mild solutions are established by using a new technical lemma for stochastic integrals with respect to TFBM in the sense of p-th moment. Moreover, based on the relations between the stochastic integrals with respect to TFBM and fractional Browni an motion, we show the continuity of mild solutions in the case of λ → 0, σ ∈ (−1/2, 0) or λ > 0, σ → σ0 ∈ (−1/2, 0). In particular, we obtain p-th moment H¨older regularity in time and p-th polynomial stability of mild solutions. This paper can be regarded as a first step to study the challenging model: stochastic 2D-Navier-Stokes equations with unbounded delay driven by tempered fractional Gaussian noise.application/pdf46 p.engAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/Stochastic Stokes equationTempered fractional Brownian motionUnbounded delayContinuity with respect to parametersHölder regularityPolynomial stabilityinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccesshttps://doi.org/10.1142/S0219493722500228