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Advances in Mathematical Fluid Mechanics
This book consists of six survey contributions that are focused on several open problems of theoretical fluid mechanics both for incompressible and compressible fluids. The first article "Viscous flows in Besov spaces" by M area Cannone ad dresses the problem of global existence of a uniquely defined solution to the three-dimensional Navier-Stokes equations for incompressible fluids. Among others the following topics are intensively treated in this contribution: (i) the systematic description of the spaces of initial conditions for which there exists a unique local (in time) solution or a unique global solution for small data, (ii) the existence of forward self-similar solutions, (iii) the r...
Mathematical Aspects of Paradoxes in Cosmology
This book provides a mathematical and numerical analysis of many problems which lead to paradoxes in contemporary cosmology, in particular, the existence of dark matter and dark energy. It is shown that these hypothetical quantities arise from excessive extrapolations of simple mathematical models to the whole physical universe. Written in a completely different style to most books on General Relativity and cosmology, the important results take the form of mathematical theorems with precise assumptions and statements. All theorems are followed by a corresponding proof, or an exact reference to the proof. Some nonstandard topics are also covered, including violation of the causality principle...
Parallel Solution of Partial Differential Equations
This IMA Volume in Mathematics and its Applications PARALLEL SOLUTION OF PARTIAL DIFFERENTIAL EQUATIONS is based on the proceedings of a workshop with the same title. The work shop was an integral part of the 1996-97IMA program on "MATHEMAT ICS IN HIGH-PERFORMANCE COMPUTING." I would like to thank Petter Bj0rstad of the Institutt for Informatikk, University of Bergen and Mitchell Luskin of the School of Mathematics, University of Minnesota for their excellent work as organizers of the meeting and for editing the proceedings. I also take this opportunity to thank the National Science Founda tion (NSF), Department of Energy (DOE), and the Army Research Office (ARO), whose financial support mad...
Applied Nonlinear Analysis
This book is meant as a present to honor Professor on the th occasion of his 70 birthday. It collects refereed contributions from sixty-one mathematicians from eleven countries. They cover many different areas of research related to the work of Professor including Navier-Stokes equations, nonlinear elasticity, non-Newtonian fluids, regularity of solutions of parabolic and elliptic problems, operator theory and numerical methods. The realization of this book could not have been made possible without the generous support of Centro de Matemática Aplicada (CMA/IST) and Fundação Calouste Gulbenkian. Special thanks are due to Dr. Ulrych for the careful preparation of the final version of this b...
Progress in Theoretical and Computational Fluid Mechanics
This volume presents a series of lectures given at the Winter School in Fluid Dynamics held in Paseky, Czech Republic in December 1993. Including original research and important new results, it contains a detailed investigation of some methods used towards the proof of global regularity for the Navier-Stokes equations. It also explores new formulations of the free-boundary in the dynamics of viscous fluids, and different methods for conservation laws in several space dimensions and related numerical schemes. The final contribution examines the existence and stability of non-isothermal compressible fluids and their relation with incompressible models.
Weak and Measure-Valued Solutions to Evolutionary PDEs
This book provides a concise treatment of the theory of nonlinear evolutionary partial differential equations. It provides a rigorous analysis of non-Newtonian fluids, and outlines its results for applications in physics, biology, and mechanical engineering.
Hudba prvočísel
Prvočísla jsou záhadná stvoření. Jejich definice je velmi jednoduchá (nejsou součinem žádného jiného přirozeného čísla kromě jedničky), ale na jejich vlastnostech je vystavěna celá matematika a jejich nevyzpytatelné chování vyvádí z míry již desítky generací nejlepších odborníků. Kromě toho má teorie prvočísel ze všech oborů čisté matematiky na moderní svět zdaleka největší praktické dopady: prostřednictvím kryptografie na ní závisejí osudy nejmocnějších států a biliony dolarů. V roce 1859 vyslovil slavný matematik Bernhard Riemann tvrzení, které s prvočísly zdánlivě vůbec nesouvisí, během let se však ukázalo, že by mohlo být pro jejich pochopení klíčové. O významu jeho hypotézy může svědčit i fakt, že je jedním ze sedmi problémů "za milion dolarů" Clayova institutu - prozatím nevyřešeným. Kniha Hudba prvočísel se věnuje historii Riemannovy hypotézy a pokusů o její řešení; přitom jakoby mimochodem probere historii moderní teorie čísel a její dopady, stranou nezůstanou ani filozofické otázky mezí poznání.Vychází ve spolupráci s nakladatelstvím Argo
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