Jiaohui Xu, Tomas Caraballo
Abstract:
We analyze the well-posedness of two versions of a stochastic time delay fractional
2D-Stokes model with nonlinear multiplicative noise.
The main tool to prove the existence and uniqueness of mild solutions is a fixed
point argument.
The results for the first model can only be proved for α in (1/2,1), and
the global existence in time is shown only when the noise is additive.
As for the second model, all results are true for α in (0,1), and the global
solutions in time is shown for general nonlinear multiplicative noise.
The analyzes for the finite and infinite delay cases, follow the
same lines, but they require different phase spaces and estimates.
This article can be considered as a first approximation to the challenging
model of stochastic time fractional Navier-Stokes
(with or without delay) which so far remains as an open problem.
Submitted April 23, 2022. Published December 21, 2022.
Math Subject Classifications: 35R11, 35Q30, 65F08, 60H15, 65F10.
Key Words: Well-posedness; stochastic time fractional 2D-Stokes equations;
mild solution; finite delay; infinite delay; multiplicative noise.
DOI: https://doi.org/10.58997/ejde.2022.86
Show me the PDF file (419 KB), TEX file for this article.
| Jiaohui Xu Dpto. Ecuaciones Diferenciales y Análisis Numérico Facultad de Matemáticas Universidad de Sevilla c/ Tarfia s/n, 41012-Sevilla, Spain email; jiaxu1@alum.us.es | |
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Tomás Caraballo Dpto. Ecuaciones Diferenciales y Análisis Numérico Facultad de Matemáticas Universidad de Sevilla c/ Tarfia s/n, 41012-Sevilla, Spain email: caraball@us.es |
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