Non-stationary Navier-Stokes Equations with Mixed Boundary Conditions

2016/11/25 by Tujin Kim, Daomin Cao, Kim, Tujin +1 · 1 citation
Engineering · Mathematics · #Fluid Dynamics and Turbulent Flows #Lattice Boltzmann Simulation Studies #Stability and Controllability of Differential Equations #math.AP #msc:35A02 #msc:35A15 #msc:35Q30 #msc:76D03 #msc:76D05

paper · pdf · doi:10.48550/arxiv.1611.08335

22 pages

arxiv created 2016/11/25 · arxiv updated 2016/11/28

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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• The steady Navier-Stokes and Stokes systems with mixed boundary conditions including one-sided leaks and pressure

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