Local Function Spaces, Heat and Navier-Stokes Equations.

Format:

Book

Author/Creator:

Triebel, Author.

Series:

EMS Tracts in Mathematics (etm) 2943-5005 20

Language:

English

Physical Description:

1 online resource (241 pages)

Place of Publication:

EMS Press 2013

System Details:

text file PDF

Summary:

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.

ISBN:

3-03719-623-8