Mild Solutions to Time Fractional Stochastic 2D-Stokes Equations with Bounded and Unbounded Delay

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...

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Detalhes bibliográficos
Autores: Xu, Jiaohui, Zhang, Zhengce, Caraballo Garrido, Tomás
Tipo de documento: artigo
Estado:Versão publicada
Data de publicação:2019
País:España
Recursos:Universidad de Sevilla (US)
Repositório:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/130371
Acesso em linha:https://hdl.handle.net/11441/130371
https://doi.org/10.1007/s10884-019-09809-3
Access Level:Acceso aberto
Palavra-chave:Well-posedness
Stochastic time fractional 2D-Stokes equations
Mild solution
Finite delay
Infinite delay
Multiplicative noise
Descrição
Resumo: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.