Local function spaces, heat and Navier-Stokes equations
By: Hans Triebel
Series: EMS tracts in mathematics -- 20; EMS tracts in mathematics -- 20.
Publisher: European Mathematical Society Publishing House
Published: 2013
Place of publication: Zürich, Switzerland
Language: eng
Number of pages: 232
ISBN-13: 9783037191231
Copyright date: 2013
Subjects: Function spaces; Heat equation; Navier-Stokes equations
Description: In this book a new approach is presented to exhibit relations between Sobolev spaces, Besov spaces, and Hölder-Zygmund spaces on the one hand and Morrey-Campanato spaces on the other. Morrey-Campanato spaces extend the notion of functions of bounded mean oscillation. These spaces play an important role in the theory of linear and nonlinear PDEs. Chapters 1-3 deal with local smoothness spaces in Euclidean n-space based on the Morrey-Campanato refinement of the Lebesgue spaces. The presented approach relies on wavelet decompositions. This is applied in Chapter 4 to Gagliardo-Nirenberg inequalities. Chapter 5 deals with linear and nonlinear heat equations in global and local function spaces. The obtained assertions about function spaces and nonlinear heat equations are used in Chapter 6 to study Navier-Stokes equations. The book is addressed to graduate students and mathematicians having a working knowledge of basic elements of (global) function spaces, and who are interested in applications to nonlinear PDEs with heat and Navier-Stokes equations as prototypes.
Notes: Includes bibliographical references (pages 215-227) and index.