The book develops the most recent ideas and concepts of the mathematical theory of viscous, compressible and heat conducting fluids. Two main goals are pursued: (I) global existence theory within the framework of variational (weak) solutions for the full system of the Navier-Stokes equations supplemented with large data; and (II) optimal existence results for the barotropic flows with respect to the available a priori estimates. The book is intended to be a compact and self-contained presentation of the most recent results of the mathematical theory of viscous compressible fluids. In order to...
The book develops the most recent ideas and concepts of the mathematical theory of viscous, compressible and heat conducting fluids. Two main goals ar...
The aim of this Handbook is to acquaint the reader with the current status of the theory of evolutionary partial differential equations, and with some of its applications. Evolutionary partial differential equations made their first appearance in the 18th century, in the endeavor to understand the motion of fluids and other continuous media. The active research effort over the span of two centuries, combined with the wide variety of physical phenomena that had to be explained, has resulted in an enormous body of literature. Any attempt to produce a comprehensive survey would be futile. The...
The aim of this Handbook is to acquaint the reader with the current status of the theory of evolutionary partial differential equations, and with some...
This book offers an essential introduction to the mathematical theory of compressible viscous fluids. The main goal is to present analytical methods from the perspective of their numerical applications. Accordingly, we introduce the principal theoretical tools needed to handle well-posedness of the underlying Navier-Stokes system, study the problems of sequential stability, and, lastly, construct solutions by means of an implicit numerical scheme. Offering a unique contribution by exploring in detail the synergy of analytical and numerical methods the book offers a valuable resource for...
This book offers an essential introduction to the mathematical theory of compressible viscous fluids. The main goal is to present analytical method...
Many problems in mathematical fluid dynamics involve the behavior of solutions of nonlinear systems of partial differential equations. This book is an introduction to the problems involving singular limits based on the concept of weak or variational solutions.
Many problems in mathematical fluid dynamics involve the behavior of solutions of nonlinear systems of partial differential equations. This book is an...
The series is devoted to the publication of high-level monographs and specialized graduate texts which cover the whole spectrum of applied mathematics, including its numerical aspects. The focus of the series is on the interplay between mathematical and numerical analysis, and also on its applications to mathematical models in the physical and life sciences.
The aim of the series is to be an active forum for the dissemination of up-to-date information in the form of authoritative works that will serve the applied mathematics community as the basis for further research.
The series is devoted to the publication of high-level monographs and specialized graduate texts which cover the whole spectrum of applied mathemat...
The main goal of this book is to provide an overview of the state of the art in the mathematical modeling of complex fluids, with particular emphasis on its thermodynamical aspects. The central topics of the text, the modeling, analysis and numerical simulation of complex fluids, are of great interest and importance both for the understanding of various aspects of fluid dynamics and for its applications to special real-world problems. New emerging trends in the subject are highlighted with the intent to inspire and motivate young researchers and PhD students.
The main goal of this book is to provide an overview of the state of the art in the mathematical modeling of complex fluids, with particular emphas...
