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arXiv · 1611.08335

Non-stationary Navier-Stokes Equations with Mixed Boundary Conditions

Tujin Kim·Daomin Cao
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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.

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Tujin Kim, Daomin Cao. 2016-11-25. Non-stationary Navier-Stokes Equations with Mixed Boundary Conditions. https://arxiv.org/abs/1611.08335

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