Local function spaces, heat and Navier-Stokes equations / Hans Triebel.

Format:

Book

Author/Creator:

Triebel, Hans, author.

Series:

EMS tracts in mathematics ; 20.

EMS tracts in mathematics ; 20

Language:

English

Subjects (All):

Function spaces.

Heat equation.

Navier-Stokes equations.

Physical Description:

ix, 232 pages : illustration ; 25 cm.

Place of Publication:

Zürich, Switzerland : European Mathematical Society Publishing House, [2013]

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.

Contents:

1. Global and local spaces

2. Local spaces: properties

3. Morrey-Campanato spaces

4. Galiardo-Nirenberg inequalities

5. Heat equations

6, Navier-Stokes equations.

Notes:

Includes bibliographical references (pages 215-227) and index.

ISBN:

9783037191231

3037191236

OCLC:

851417358

Online:

Volltext