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By Frédéric Alliot, Cherif Amrouche (auth.), Adélia Sequeira, Hugo Beirão da Veiga, Juha Hans Videman (eds.)

This ebook is intended as a gift to honor Professor at the th celebration of his 70 birthday. It collects refereed contributions from sixty-one mathematicians from 11 international locations. They disguise many various parts of study concerning the paintings of Professor together with Navier-Stokes equations, nonlinear elasticity, non-Newtonian fluids, regularity of options of parabolic and elliptic difficulties, operator conception and numerical tools. the conclusion of this publication couldn't were made attainable with out the beneficiant help of Centro de Matemática Aplicada (CMA/IST) and Fundação Calouste Gulbenkian. certain thank you are as a result of Dr. Ulrych for the cautious coaching of the ultimate model of this booklet. final yet no longer least, we want to exhibit our gratitude to Dr. for her precious the aid of the very starting. This undertaking couldn't were effectively concluded with out her enthusiasm and loving deal with her father. On behalf of the editors ADÉLIA SEQUEIRA v venerated by way of the Order of benefit of the Czech Republic by way of Václav Havel, President of the Czech Republic, at the October 28, 1998, Professor Emeritus of arithmetic on the Charles college in Prague, Presidential study Professor on the Northern Illinois college and health professional Honoris Causa on the Technical college of Dresden, has been enriching the Czech and global arithmetic along with his new rules within the components of partial differential equations, nonlinear practical research and functions of the either disciplines in continuum mechanics and hydrodynamics for greater than 40 years.

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Univ. Padova, 31:308-340. , Meyer, Y. and Semmes, S. (1993). Compensated compactness and Hardy spaces. J. Math. , 72(3):247-286. P. (1994). An introduction to the mathematical theory of the NavierStokes equations, volume II. Springer tracts in natural philosophy. [9] Girault, V. and Sequeira, A. (1991). A well posed problem for the exterior Stokes equations in two and three dimensions. Arch. Rational Mech. , 114:313-333. [10] Girault, V. A. (1986). Finite Element Approximation of the Navier-Stokes Equations.

2. 3 that we can associate with each weak solution u a pressure that locally belongs to But, we do not have yet any information concerning the integrability at infinity of Our first result is dedicated to this question. 3. 3 has a representative such that with Proof. 3 and let be the associated pressure. 1. 2 yields besides that so we get that and ii) We consider now the other terms of Since is bounded and has bounded derivatives with compact support, it is easy to check that the terms and belong to Proving that is even simpler.

Indiana Univ. Math. , 40:1-25. [12] Kozono, H. and Sohr, H. (1992). On a new class of generalized solutions for the Stokes equations in exterior domains. Ann. Scuola Norm. Sup. Pisa, Ser. IV, 19:155-181. [13] Leray, J. (1934). Sur le mouvement d’un liquide visqueux emplissant l’espace. , 63:193-248. [14] Nirenberg, L. (1959). On elliptic partial differential equations. Ann. Scuola Norm. Sup. Pisa, 13:116-162. [15] Specovius Neugebauer, M. (1994). Weak Solutions of the Stokes Problem in Weighted Sobolev Spaces.

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