A remark on the Stokes problem in Lorentz spaces

Paolo Maremonti

doi:10.3934/dcdss.2013.6.1323

Article Contents

2013, Volume 6, Issue 5: 1323-1342. Doi: 10.3934/dcdss.2013.6.1323

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A remark on the Stokes problem in Lorentz spaces

Paolo Maremonti^1,

1.
Dipartimento di Matematica, Università degli Studi di Napoli, via Vivaldi, 43, I-81100 Caserta

Received: November 30, 2011

Revised: January 31, 2012

Published: September 2013

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Abstract

We study the Stokes initial boundary value problem with an initial data in a Lorentz space. We develop a suitable technique able to solve the problem and to prove the semigroup properties of the resolving operator in the case of the ''limit exponents''. The results are a completion of the ones related to the usual $L^p$-theory, of the ones already known and they are also useful tool to study some questions related to the Navier-Stokes equations.

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

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