Non-stationary Navier-Stokes Equations with Mixed Boundary Conditions
Vol. 24 (2017), No. 2, Page 159–194.
Kim, Tujin ; Cao, Daomin
Non-stationary Navier-Stokes Equations with Mixed Boundary Conditions
[Full Article (PDF)] [MathSciNet Review (HTML)] [MathSciNet Review (PDF)]
Abstract:
In this paper we are concerned with the initial boundary value problem of the 2, 3-D Navier-Stokes equations with mixed boundary conditions including conditions for velocity, static pressure, stress, rotation and Navier slip condition together. Under a compatibility condition at the initial instance it is proved that for the small data there exists a unique solution on the given interval of time. Also, it is proved that if a solution is given, then there exists a unique solution for small perturbed data satisfying the compatibility condition. Our smoothness condition for initial functions in the compatibility condition is weaker than one in such a previous result.
Keywords: Navier-Stokes equations, Pressure, Stress, Rotation, Slip, Mixed boundary conditions, Mixed problem, Unique existence.
Mathematics Subject Classification (2010): 35Q30, 35A02, 35A15, 76D03, 76D05.
Mathematical Reviews Number: MR3674446
Received: 2016-02-23
