摩擦型滑移或泄漏边界条件下非定常Navier-斯托克斯方程的强解
On a strong solution of the non-stationary Navier-Stokes equations under slip or leak boundary conditions of friction type
摘要：
研究了非线性滑移或泄漏边界条件下非定常Navier-斯托克斯方程的强解。我们证明了问题是由一个抛物型变分不等式来表示的，并证明了该变分不等式的唯一性。利用Galerkin方法和得到的先验估计，我们分别证明了二维和三维滑移问题解的整体和局部存在性。对于泄漏问题，在$t=0$无泄漏的假设下，我们证明了局部存在的二维和三维的情况下。初态的相容性条件在估计中起着重要的作用。
英文摘要：
Strong solutions of the non-stationary Navier-Stokes equations under non-linearized slip or leak boundary conditions are investigated. We show that the problems are formulated by a variational inequality of parabolic type, to which uniqueness is established. Using Galerkin's method and deriving a priori estimates, we prove global and local existence for 2D and 3D slip problems respectively. For leak problems, under no-leak assumption at $t=0$ we prove local existence in 2D and 3D cases. Compatibility conditions for initial states play a significant role in the estimates.
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