Hybrid Function Spaces, Heat and Navier-Stokes Equations.

Format:

Book

Author/Creator:

Triebel, Author.

Series:

EMS Tracts in Mathematics (etm) 2943-5005 24

Language:

English

Physical Description:

1 online resource (196 pages)

Place of Publication:

EMS Press 2015

System Details:

text file PDF

Summary:

This book is the continuation of _Local Function Spaces, Heat and Navier-Stokes Equations_ (Tracts in Mathematics 20, 2013) by the author. 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 a crucial role in the theory of linear and nonlinear PDEs. Chapter 1 (Introduction) describes the main motivations and intentions of this book. Chapter 2 is a selfcontained introduction into Morrey spaces. Chapter 3 deals with hybrid smoothness spaces (which are between local and global 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 linear and nonlinear heat equations in global and hybrid spaces. The obtained assertions about function spaces and nonlinear heat equations are used in the Chapters 5 and 6 to study Navier-Stokes equations in hybrid and global spaces. This 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.

ISBN:

3-03719-650-5