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Hans Triebel (University of Jena, Germany)
Local Function Spaces, Heat and Navier–Stokes Equations
ISBN print 978-3-03719-123-1, ISBN online 978-3-03719-623-6DOI 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