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Abstract:  Before getting into the main topic, I will first briefly explain the Navier-Stokes equations and remind you of some basic tools that we need, such as Sobolev inequality, the Sobolev embedding theorem, Poincare's inequality and the Leray-Schauder theorem. Then we will establish, as main theorems, existence and uniqueness of a generalized solution to the stationary Navier-Stokes equations with homogenous boundary condition on a bounded or unbounded domain.

This talk relies on Ladyzhenskaya’s book on the Naiver-Stokes equations.