The continuity, regularity and polynomial stability of mild solutions for stochastic 2D-Stokes equations with unbounded delay driven by tempered fractional Gaussian noise
We 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...
| Authors: | , , |
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| Format: | article |
| Status: | Versión enviada para evaluación y publicación |
| Publication Date: | 2021 |
| Country: | España |
| Institution: | Universidad de Sevilla (US) |
| Repository: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/137514 |
| Online Access: | https://hdl.handle.net/11441/137514 https://doi.org/10.1142/S0219493722500228 |
| Access Level: | Open access |
| Keyword: | Stochastic Stokes equation Tempered fractional Brownian motion Unbounded delay Continuity with respect to parameters Hölder regularity Polynomial stability |
| Summary: | We 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. |
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