Large-eigenvalue global existence and regularity results for the Navier-Stokes equation
type: Item
instance of: scholarly article
title: Large-eigenvalue global existence and regularity results for the Navier-Stokes equation
zbMATH Open document ID: 0863.35075
published in: Journal of Differential Equations
publication date: 1997-06-03T00:00:00Z
review text: The author develops integral-equation techniques to obtain some results in the case of purely homogeneous-Dirichlet boundary conditions. The role of the thinness of the domain is replaced by the reciprocal of the first eigenvalue of the Laplacian. It is also shown the utility of the integral-equation techniques by bootstrapping global \(H^1\)-bounds, whenever available in 2D or 3D, into higher-order global bounds with slightly smoother forcing functions than those assumed by \textit{C. Guillopé} [Ann. Inst. Fourier 32, No. 3, 1-37 (1982; Zbl 0497.35075)], but otherwise more general, in that \(L^p\)-integrable singularities in time are allowed.
reviewed by: Fabio Rosso
Mathematics Subject Classification ID: 35Q30
Mathematics Subject Classification ID: 35A05
Mathematics Subject Classification ID: 35B65
zbMATH DE Number: 885506
zbMATH Keywords: integral-equation techniques
zbMATH Keywords: homogeneous-Dirichlet boundary conditions
zbMATH Keywords: first eigenvalue of the Laplacian
zbMATH Keywords: global bounds
author: Joel Avrin
MaRDI profile type: Publication
full work available at URL: jdeq.1996.0074
OpenAlex ID: W1975349239
DOI: 10.1006/JDEQ.1996.0074
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description: scientific article; zbMATH DE number 885506