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

Chérif Amrouche; Mohamed Meslameni; Šárka Nečasová

doi:10.3934/dcdss.2014.7.901

Article Contents

2014, Volume 7, Issue 5: 901-916. Doi: 10.3934/dcdss.2014.7.901

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

1.
Laboratoire de Mathématiques et de leurs Applications, CNRS UMR 5142, Université de Pau et des Pays de l'Adour, 64013 Pau
2.
Mathematical Institute, Academy of Sciences of the Czech Republic, Žitná 25, 115 67 Praha 1

Received: April 2013

Published: October 2014

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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.

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Mathematics Subject Classification: 35Q30, 76D03, 76D05, 76D07.

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References

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