Chapman & Hall/CRC Research Notes in Mathematics

5 primary works

Recent Developments in Theoretical Fluid Mechanics

by G.P. Galdi and J. Necas

Published 23 August 1993

Including previously unpublished, original research material, this comprehensive book analyses topics of fundamental importance in theoretical fluid mechanics. The five papers appearing in this volume are centred around the mathematical theory of the Navier-Stokes equations (incompressible and compressible) and certain selected non-Newtonian modifications.

Progress in Theoretical and Computational Fluid Mechanics

by G.P. Galdi, Jindrich Necas, and Josef Malek

Published 18 May 1994

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.

Mathematical Theory in Fluid Mechanics

by G.P. Galdi, Josef Malek, and J. Necas

Published 1 August 1996

This volume consists of four contributions that are based on a series of lectures delivered by Jens Frehse. Konstantin Pikeckas, K.R. Rajagopal and Wolf von Wahl t the Fourth Winter School in Mathematical Theory in Fluid Mechanics, held in Paseky, Czech Republic, from December 3-9, 1995. In these papers the authors present the latest research and updated surveys of relevant topics in the various areas of theoretical fluid mechanics.

Specifically, Frehse and Ruzicka study the question of the existence of a regular solution to Navier-Stokes equations in five dimensions by means of weighted estimates. Pileckas surveys recent results regarding the solvability of the Stokes and Navier-Stokes system in domains with outlets at infinity. K.R. Rajagopal presents an introduction to a continuum approach to mixture theory with the emphasis on the constitutive equation, boundary conditions and moving singular surface. Finally, Kaiser and von Wahl bring new results on stability of basic flow for the Taylor-Couette problem in the small-gap limit. This volume would be indicated for those in the fields of applied mathematicians, researchers in fluid mechanics and theoretical mechanics, and mechanical engineers.

Advanced Topics in Theoretical Fluid Mechanics

by J. Malek, Jindrich Necas, and Mirko Rokyta

Published 15 August 1998

This volume consists of contributions based on a series of lectures delivered at the Fifth Winter School on Mathematical Theory in Fluid Mechanics, held in Paseky nad Jizerou, Czech Republic. The contributions are written by the main lecturers of the school and cover several significant topics in the field of theoretical fluid mechanics.

Specifically, Professor Bardos presents mathematical studies of various evolutionary models of fluids that capture the motions of gases and liquids on different scales, from molecules and rarefied gases, to fluids and gases at the continuum level, and finally to fluids in turbulent regimes. In addition to discussing the mathematical analysis of particular systems on their own, Professor Bardos devotes a great deal of attention to the passage from one scale to another.

Professor Dafermos provides an introduction to the foundation of classical continuum physics, built on a precise and general mathematical basis that enables one to present arguments in a very transparent way. Professor Novotn*y systematically investigates the properties of the steady-state transport equations, with emphasis on flows in exterior domains. Finally, Professor Solonnikov illustrates his approach to the non-simple analysis of free boundary problems in fluid mechanics using three model examples for the steady-state Navier-Stokes equations.

Partial Differential Equations

by J. Necas

Published 23 July 1999

As a satellite conference of the 1998 International Mathematical Congress and part of the celebration of the 650th anniversary of Charles University, the Partial Differential Equations Theory and Numerical Solution conference was held in Prague in August, 1998. With its rich scientific program, the conference provided an opportunity for almost 200 participants to gather and discuss emerging directions and recent developments in partial differential equations (PDEs).
This volume comprises the Proceedings of that conference. In it, leading specialists in partial differential equations, calculus of variations, and numerical analysis present up-to-date results, applications, and advances in numerical methods in their fields. Conference organizers chose the contributors to bring together the scientists best able to present a complex view of problems, starting from the modeling, passing through the mathematical treatment, and ending with numerical realization. The applications discussed include fluid dynamics, semiconductor technology, image analysis, motion analysis, and optimal control.
The importance and quantity of research carried out around the world in this field makes it imperative for researchers, applied mathematicians, physicists and engineers to keep up with the latest developments. With its panel of international contributors and survey of the recent ramifications of theory, applications, and numerical methods, Partial Differential Equations: Theory and Numerical Solution provides a convenient means to that end.