### Abstract

We consider the stationary Navier-Stokes equations on a multiply connected bounded domain Ω in R{double-struck}^{n} for n = 2; 3 under nonhomogeneous boundary conditions. We present a new sufficient condition for the existence of weak solutions. This condition is a variational estimate described in terms of the harmonic part of solenoidal extensions of the given boundary data; we prove it by using the Helmholtz-Weyl decomposition of vector fields over Ω satisfying adequate boundary conditions. We also study the validity of Leray's inequality for various assumptions about the symmetry of Ω.

Original language | English |
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Pages (from-to) | 127-150 |

Number of pages | 24 |

Journal | Pacific Journal of Mathematics |

Volume | 243 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2009 Nov 1 |

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### Keywords

- Helmholtz-Weyl decomposition
- Nonhomogeneous Boundary value problems
- Stationary Navier-Stokes equations

### ASJC Scopus subject areas

- Mathematics(all)