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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Regularity criteria involving the pressure for the weak solutions to the Navier-Stokes equations


Authors: Luigi C. Berselli and Giovanni P. Galdi
Journal: Proc. Amer. Math. Soc. 130 (2002), 3585-3595
MSC (2000): Primary 35B65; Secondary 35K55, 76D05
Published electronically: July 2, 2002
MathSciNet review: 1920038
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Abstract: In this paper we consider the Cauchy problem for the $n$-dimensional Navier-Stokes equations and we prove a regularity criterion for weak solutions involving the summability of the pressure. Related results for the initial-boundary value problem are also presented.


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Additional Information

Luigi C. Berselli
Affiliation: Dipartimento di Matematica Applicata “U.Dini”, Università di Pisa, Via Bonanno 25/b, 56126 Pisa, Italy
Email: berselli@dma.unipi.it

Giovanni P. Galdi
Affiliation: Department of Mechanical Engineering, University of Pittsburgh, Pittsburgh, Pennsylvannia 15260
Email: galdi@engrng.pitt.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-02-06697-2
PII: S 0002-9939(02)06697-2
Received by editor(s): June 18, 2001
Published electronically: July 2, 2002
Additional Notes: The first author was partially supported by the the MURST project: “Theory and Applications of Linear and Nonlinear Hyperbolic Equations".
Communicated by: David S. Tartakoff
Article copyright: © Copyright 2002 American Mathematical Society