By Adélia Sequeira, Hugo Beirão da Veiga, Juha H. Videman
This publication is intended as a gift to honor Professor at the th party of his 70 birthday. It collects refereed contributions from sixty-one mathematicians from 11 international locations. They conceal many alternative parts of analysis regarding the paintings of Professor together with Navier-Stokes equations, nonlinear elasticity, non-Newtonian fluids, regularity of ideas of parabolic and elliptic difficulties, operator thought and numerical tools. the belief of this booklet 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 education of the ultimate model of this ebook. final yet now not least, we want to show our gratitude to Dr. for her worthwhile the aid of the very starting. This undertaking couldn't were effectively concluded with no her enthusiasm and loving deal with her father. On behalf of the editors ADÉLIA SEQUEIRA v venerated via the Order of advantage 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 collage in Prague, Presidential learn Professor on the Northern Illinois collage and health practitioner Honoris Causa on the Technical collage of Dresden, has been enriching the Czech and international arithmetic together with his new rules within the components of partial differential equations, nonlinear useful research and functions of the either disciplines in continuum mechanics and hydrodynamics for greater than 40 years.
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SOME LEMMAS In this section we present the results needed for the proof of Theorem. 3) holds. Lemma 1. ( Let to the system (4-1)- Then for each be a weak solution holds. Lemma 2. () Let be a nonnegative function and let A, B, C, a, b be nonnegative constants. Suppose that for all and all holds. 4 from the paper . Lemma 3.
Amrouche-Girault ) Let domain with boundary. Let and assume that Find be a bounded with Then, the problem: such that has a unique solution such that If f and to then and also belong to moreover belong The Stokes problem in the whole space has been recently much studied in various functional spaces (see for instance Borchers-Miyakawa , Girault-Sequeira , Kozono-Sohr [11, 12] or Specovius Neugebauer ). The authors have also provided a rather complete study of this problem in weighted Sobolev spaces in .
10] Girault, V. A. (1986). Finite Element Approximation of the Navier-Stokes Equations. Theory and Algorithms. Springer-Verlag, Berlin.  Kozono, H. and Sohr, H. (1991). New a priori estimates for the Stokes equations in exteriors domains. Indiana Univ. Math. , 40:1-25.  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.  Leray, J. (1934). Sur le mouvement d’un liquide visqueux emplissant l’espace.
Applied nonlinear analysis by Adélia Sequeira, Hugo Beirão da Veiga, Juha H. Videman