Wow! eBook
Local Function Spaces, Heat and Navier-stokes Equations
Author(s): Hans Triebel (Author)
- Publisher: European Mathematical Society
- Publication Date: May 15, 2013
- Language: English
- Print length: 241 pages
- ISBN-10: 3037191236
- ISBN-13: 9783037191231
Book 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 -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 with a working knowledge of basic elements of (global) function spaces and an interest in applications to nonlinear PDEs with heat and Navier-Stokes equations as prototypes. A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society.
