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Journal of Mathematical Fluid Mechanics

, Volume 19, Issue 4, pp 819–829 | Cite as

Existence and Uniqueness of Very Weak Solutions to the Steady-State Navier–Stokes Problem in Lipschitz Domains

  • Vincenzo CosciaEmail author
Article

Abstract

We prove that in a bounded Lipschitz domain of \({\mathbb {R}}^3\) the steady-state Navier–Stokes equations with boundary data in \(L^2(\partial \Omega )\) have a very weak solution \(\varvec{u}\in L^3(\Omega )\), unique for large viscosity.

Keywords

Stationary Navier Stokes equations Bounded Lipschitz domains Boundary-value problem 

Mathematics Subject Classification

Primary 76D05 35Q30 Secondary 31B10 76D03 

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Copyright information

© Springer International Publishing 2016

Authors and Affiliations

  1. 1.Dipartimento di Matematica e InformaticaUniversità di FerraraFerraraItaly

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