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

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Abstract

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.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, 710049, Shaanxi, China

    Yanren Hou & Shuaichao Pei

Authors
  1. Yanren Hou
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  2. Shuaichao Pei
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Correspondence to Yanren Hou.

Additional information

Subsidized by NSFC (Grant No. 11571274 & 11171269) and the Ph.D. Programs Foundation of Ministry of Education of China (Grant No. 20110201110027)

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Hou, Y., Pei, S. On the weak solutions to steady Navier-Stokes equations with mixed boundary conditions. Math. Z. 291, 47–54 (2019). https://doi.org/10.1007/s00209-018-2072-7

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  • DOI: https://doi.org/10.1007/s00209-018-2072-7

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