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Chen, Siran Li, Zhongmin Qian","submitted_at":"2018-12-17T00:14:42Z","abstract_excerpt":"We are concerned with the inviscid limit of the Navier-Stokes equations on bounded regular domains in $\\mathbb{R}^3$ with the kinematic and Navier boundary conditions. We first establish the existence and uniqueness of strong solutions in the class $C([0,T_\\star); H^r(\\Omega; \\mathbb{R}^3)) \\cap C^1([0,T_\\star); H^{r-2}(\\Omega;\\mathbb{R}^3))$ with some $T_\\star>0$ for the initial-boundary value problem with the kinematic and Navier boundary conditions on $\\partial \\Omega$ and divergence-free initial data in the Sobolev space $H^r(\\Omega; \\mathbb{R}^3)$ for $r\\geq 2$. 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