Mathematische Zeitschrift

, Volume 291, Issue 1–2, pp 47–54 | Cite as

On the weak solutions to steady Navier-Stokes equations with mixed boundary conditions

  • Yanren HouEmail author
  • Shuaichao Pei


In this paper, for the Navier-Stokes equations in a bounded connected polygon or polyhedron \(\Omega \subset R^d\), \(d=2,3\), with a homogenous stress type mixed boundary condition, we establish an a priori estimate for the weak solutions and the existence result without small data and/or large viscosity restriction. And a global uniqueness result is obvious based on the a priori estimate obtained.


Navier-Stokes equations Mixed boundary conditions A priori estimate Existence Global uniqueness 


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsXi’an Jiaotong UniversityXi’anChina

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