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Discrete and Continuous Dynamical Systems - Series S (DCDS-S)
 

Linearized Navier-Stokes equations in $\mathbb{R}^3$: An approach in weighted Sobolev spaces

Pages: 901 - 916, Volume 7, Issue 5, October 2014      doi:10.3934/dcdss.2014.7.901

 
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Chérif Amrouche - Laboratoire de Mathématiques et de leurs Applications, CNRS UMR 5142, Université de Pau et des Pays de l'Adour, 64013 Pau, France (email)
Mohamed Meslameni - Laboratoire de Mathématiques et de leurs Applications, CNRS UMR 5142, Université de Pau et des Pays de l'Adour, 64013 Pau, France (email)
Šárka Nečasová - Mathematical Institute, Academy of Sciences of the Czech Republic, Žitná 25, 115 67 Praha 1, Czech Republic (email)

Abstract: In this work, we study the linearized Navier-Stokes equations in $\mathbb{R}^3$, the Oseen equations. We are interested in the existence and the uniqueness of generalized and strong solutions in $L^p$-theory which makes analysis more difficult. Our approach rests on the use of weighted Sobolev spaces.

Keywords:  Generalized Oseen equations, weighted Sobolev spaces, the existence, the uniqueness, generalized solutions, strong solutions.
Mathematics Subject Classification:  35Q30, 76D03, 76D05, 76D07.

Received: April 2013;      Available Online: May 2014.

 References