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

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Abstract

Following the ideas developed in Girinon (Annales de l’Institut Poincaré. Analyse Non Linéaire 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.

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Authors and Affiliations

  1. Institut de Mathématiques, UMR CNRS 5219, Université Paul Sabatier, 31062, Toulouse Cedex 9, France

    Vincent Girinon

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  1. Vincent Girinon
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Correspondence to Vincent Girinon.

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Communicated by I. Straskraba

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Girinon, V. Navier–Stokes Equations with Nonhomogeneous Boundary Conditions in a Bounded Three-Dimensional Domain. J. Math. Fluid Mech. 13, 309–339 (2011). https://doi.org/10.1007/s00021-009-0018-x

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  • DOI: https://doi.org/10.1007/s00021-009-0018-x

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