# Local Function Spaces, Heat and Navier–Stokes Equations

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*Hans Triebel*

A publication of the European Mathematical Society

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
with a working knowledge of basic elements of (global) function
spaces and an interest 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.