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Following the standard strategy of deriving the solutions in a Gubser flow, we take the Weyl rescaling and obtain the energy-momentum and angular momentum conversation equations in the $dS_{3}\\times\\mathbb{R}$ space-time. We then derive the analytic solutions of spin density, spin potential and other thermodynamic in $dS_{3}\\times\\mathbb{R}$ space-time and transform them back into Minkowski space-time $\\mathbb{R}^{3,1}$. 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