# 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.