## On the Existence of Solutions of the Steady-state Navier-Stokes Equations for a Class of Non-smooth Boundary Data |

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### Contents

iii Case of an Isolated Singular Point | 31 |

Section 3 Existence Theory | 65 |

Appendix A Specific Example of Hopf Function | 119 |

2 other sections not shown

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### Common terms and phrases

angle approximating solution arbitrary arc length assume axis boundary data boundary value problem bounded subdomain check the behavior cn+h(v compact support Cone consider constant contact of order convex cp cos ncp cp sin ncp curl _ curves and isolated defined Definition denote derivatives Dirichlet integral distance Euclidean distance extend exterior Navier-Stokes exterior problem Finn fluid Fujita Green's tensor Hence Holder continuous inequality inside Sp interior intersects isolated singular point Jacobian Navier-Stokes boundary value Navier-Stokes equations Navier-Stokes problem neighborhood obtain Odqvist proof rt(w ruled surface satisfying Condition Section singular curve smooth function smooth portion solenoidal extension field solenoidal vector field ß cos nß ß sin nß surface normal surface singularity T'G dS tangent Theorem 2.1 Theorem 3-6 transformation vector field vector function Vu|2 dy Vw(x weak equation zero Уф фП