Article
Mild Solutions to Time Fractional Stochastic 2D-Stokes Equations with Bounded and Unbounded Delay
Author/s | Xu, Jiaohui
Zhang, Zhengce Caraballo Garrido, Tomás |
Department | Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico |
Publication Date | 2019-11-19 |
Deposit Date | 2022-03-03 |
Published in |
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Abstract | In this paper, the well-posedness of stochastic time fractional 2D-Stokes equations of order α ∈ (0, 1) containig finite or infinite delay with multiplicative noise is established, respectively, in the spaces C([−h, 0]; ... In this paper, the well-posedness of stochastic time fractional 2D-Stokes equations of order α ∈ (0, 1) containig finite or infinite delay with multiplicative noise is established, respectively, in the spaces C([−h, 0]; L2(Ω; L2 σ )) and C((−∞, 0]; L2(Ω; L2 σ )). The existence and uniqueness of mild solution to such kind of equations are proved by using a fixed-point argument. Also the continuity with respect to initial data is shown. Finally, we conclude with several comments on future research concerning the challenging model: time fractional stochastic delay 2D-Navier–Stokes equations with multiplicative noise. Hence, this paper can be regarded as a first step to study this challenging topic. |
Citation | Xu, J., Zhang, Z. y Caraballo Garrido, T. (2019). Mild Solutions to Time Fractional Stochastic 2D-Stokes Equations with Bounded and Unbounded Delay. Journal of Dynamics and Differential Equations, 22 (34), 583-603. |
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