**EMS Tracts in Mathematics**

Volume: 22;
2015;
196 pp;
Hardcover

MSC: Primary 46; 42; 35; 76;
**Print ISBN: 978-3-03719-150-7
Product Code: EMSTM/22**

List Price: $64.00

Individual Member Price: $51.20

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# Hybrid Function Spaces, Heat and Navier–Stokes Equations

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*Hans Triebel*

A publication of the European Mathematical Society

This book is the continuation of *Local Function Spaces,
Heat and Navier–Stokes Equations* (EMS Tracts in
Mathematics, volume 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 self-contained introduction to 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, which relies on wavelet decompositions, 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 Chapters 5 and 6 to study Navier–Stokes equations in hybrid and global spaces.

This book is addressed to graduate students and mathematicians who have 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.

A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society.

#### Readership

Graduate students and research mathematicians interested in function spaces, Morrey spaces, heat equations, and Navier–Stokes equations.