Well-posedness of stochastic time fractional 2D-Stokes models with finite and infinite delay

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dc.contributor.authorXu, Jiaohui
dc.contributor.authorCaraballo, Tomas
dc.date.accessioned2023-05-15T21:01:41Z
dc.date.available2023-05-15T21:01:41Z
dc.date.issued2022-12-21
dc.description.abstractWe 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.
dc.description.departmentMathematics
dc.formatText
dc.format.extent29 pages
dc.format.medium1 file (.pdf)
dc.identifier.citationXu, J., & Caraballo, T. (2022). Well-posedness of stochastic time fractional 2D-Stokes models with finite and infinite delay. <i>Electronic Journal of Differential Equations, 2022</i>(86), pp. 1-29.
dc.identifier.issn1072-6691
dc.identifier.urihttps://hdl.handle.net/10877/16810
dc.language.isoen
dc.publisherTexas State University, Department of Mathematics
dc.rightsAttribution 4.0 International
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.sourceElectronic Journal of Differential Equations, 2022, San Marcos, Texas: Texas State University and University of North Texas.
dc.subjectWell-posedness
dc.subjectStochastic time fractional 2D-Stokes equations
dc.subjectMild solution
dc.subjectFinite delay
dc.subjectInfinite delay
dc.subjectMultiplicative noise
dc.titleWell-posedness of stochastic time fractional 2D-Stokes models with finite and infinite delay
dc.typeArticle

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