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June  2010, 3(2): 199-219. doi: 10.3934/dcdss.2010.3.199

An elementary approach to the 3D Navier-Stokes equations with Navier boundary conditions: Existence and uniqueness of various classes of solutions in the flat boundary case.

Luigi C. Berselli 1,

1. 

Dipartimento di Matematica Applicata "U. Dini”, Via F. Buonarroti 1/c, I-56127, Pisa, Italy

Received  February 2009 Revised  June 2009 Published  April 2010

We study with elementary tools the stationary 3D Navier-Stokes equations in a flat domain, equipped with Navier (slip without friction) boundary conditions. We prove existence and uniqueness of weak, strong, and very-weak solutions in appropriate Banach spaces and most of the result hold true without restrictions on the size of the data. Results are partially known, but our approach allows us to give rather elementary and self-contained proofs.
Keywords: Navier's boundary conditions, $L^q$-theory, Stokes and Navier-Stokes equations, very-weak solutions..
Mathematics Subject Classification: Primary: 35Q30; Secondary: 76D0.
Citation: Luigi C. Berselli. An elementary approach to the 3D Navier-Stokes equations with Navier boundary conditions: Existence and uniqueness of various classes of solutions in the flat boundary case.. Discrete and Continuous Dynamical Systems - S, 2010, 3 (2) : 199-219. doi: 10.3934/dcdss.2010.3.199
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