Artículo
The continuity, regularity and polynomial stability of mild solutions for stochastic 2D-Stokes equations with unbounded delay driven by tempered fractional Gaussian noise
Autor/es | Liu, Yarong
Wang, Yejuan Caraballo Garrido, Tomás |
Departamento | Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico |
Fecha de publicación | 2021-09 |
Fecha de depósito | 2022-09-30 |
Publicado en |
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Resumen | 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 ... 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. |
Cita | Liu, 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. |
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