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Local Function Spaces, Heat and Navier–Stokes Equations
EMS Tracts in Mathematics Vol. 20

Hans Triebel (University of Jena, Germany)

Local Function Spaces, Heat and Navier–Stokes Equations

ISBN print 978-3-03719-123-1, ISBN online 978-3-03719-623-6
DOI 10.4171/123
May 2013, 241 pages, hardcover, 17 x 24 cm.
64.00 Euro

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.

Keywords: Function spaces, Morrey–Campanato spaces, Gagliardo–Nirenberg inequalities, heat equations, Navier–Stokes equations

Further Information

Review zbMATH 1280.46002

Review in MR 3086433