By Adélia Sequeira, Hugo Beirão da Veiga, Juha H. Videman
This ebook 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 nations. They hide many various components of analysis on the topic of the paintings of Professor together with Navier-Stokes equations, nonlinear elasticity, non-Newtonian fluids, regularity of ideas of parabolic and elliptic difficulties, operator idea 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. targeted thank you are as a result of Dr. Ulrych for the cautious instruction of the ultimate model of this e-book. final yet no longer least, we want to convey our gratitude to Dr. for her precious 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 commemorated via 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 collage in Prague, Presidential study Professor on the Northern Illinois collage and medical professional Honoris Causa on the Technical college of Dresden, has been enriching the Czech and global arithmetic together with his new principles within the parts of partial differential equations, nonlinear useful research and purposes of the either disciplines in continuum mechanics and hydrodynamics for greater than 40 years.
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Extra resources for Applied nonlinear analysis
3 and prove that weak solutions are also more regular. As in the previous paragraph, we consider separately the regularity near the boundary and near infinity. Let us begin with a few properties of the non-linear term. 5. Let i) Let ii) Let be an exterior domain or then then if and if Proof. The proof relies on the Sobolev’s imbedding theorem which implies that if then and therefore by duality that On the regularity and decay of the Navier-Stokes equations... 9). and Therefore, which space is imbedded ii) Let Since we also have Since v also belongs to the GagliardoNirenberg inequalities (see for instance, Nirenberg , p.
9. Let be an exterior domain or that and satisfy the following relations hold and Assume Then, with continuous imbeddings. Proof. 15) implies that and Hölder’s inequality yields that yields that and which proves the first imbedding. , Amrouche C. 10. Let or and let _ i) Assume that weak solution be an exterior domain with boundary Then, each to the problem and the pressure satisfies has a representative such that and ii) Assume that with Then, each weak solution to the problem satisfies and the pressure has a representative such that and Proof.
4. 9. Let be an exterior domain or that and satisfy the following relations hold and Assume Then, with continuous imbeddings. Proof. 15) implies that and Hölder’s inequality yields that yields that and which proves the first imbedding. , Amrouche C. 10. Let or and let _ i) Assume that weak solution be an exterior domain with boundary Then, each to the problem and the pressure satisfies has a representative such that and ii) Assume that with Then, each weak solution to the problem satisfies and the pressure has a representative such that and Proof.