On the Ladyzhenskaya-Smagorinsky turbulence model of the Navier-Stokes equations in smooth domains. The regularity problem
type: Item
instance of: scholarly article
title: On the Ladyzhenskaya-Smagorinsky turbulence model of the Navier-Stokes equations in smooth domains. The regularity problem
zbMATH Open document ID: 1155.35073
DOI: 10.4171/JEMS/144
author: H. Beirão da Veiga
published in: Journal of the European Mathematical Society (JEMS)
publication date: 2009-02-19T00:00:00Z
full work available at URL: http://www.ems-ph.org/journals/show_pdf.php
review text: Summary: We establish regularity results up to the boundary for solutions to generalized Stokes and Navier-Stokes systems of equations in the stationary and in the evolutive cases. Generalized here means the presence of a shear dependent viscosity. We treat here the case \(p\geq 2\). Actually, we are interested in proving regularity results in \(L^q(\Omega)\) spaces for all the second order derivatives of the velocity and all the first order derivatives of the pressure. The main aim of the present paper is to extend our previous scheme, introduced by the author in earlier papers [Commun. Pure Appl. Math. 58, No. 4, 552--577 (2005; Zbl 1075.35045) and J. Math. Fluid Mech. 11, No. 2, 233--257 (2009; Zbl 1213.76047)] for the flat-boundary case, to the case of curvilinear boundaries.
Mathematics Subject Classification ID: 35Q30
Mathematics Subject Classification ID: 76D03
Mathematics Subject Classification ID: 76D05
Mathematics Subject Classification ID: 76F02
zbMATH DE Number: 5509362
MaRDI profile type: Publication
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OpenAlex ID: W2161308351
description: scientific article; zbMATH DE number 5509362