Navier–Stokes Equations with Nonhomogeneous Boundary Conditions in a Bounded Three-Dimensional Domain

Abstract

Following the ideas developed in Girinon (Annales de l’Institut Poincare. Analyse Non Lineaire 26:2025–2053, 2009), we prove the existence of a weak solution to Navier–Stokes equations describing the isentropic flow of a gas in a bounded region, \({\Omega\subset \mathbf{R}^{3}}\) , with nonhomogeneous Dirichlet boundary conditions on ∂Ω.