EMS Tracts in Mathematics
Volume: 20; 2013; 241 pp; Hardcover
MSC: Primary 46; 42; 35; 76;
Print ISBN: 978-3-03719-123-1
Product Code: EMSTM/20
List Price: $84.00
Individual Member Price: $67.20
Local Function Spaces, Heat and Navier–Stokes EquationsShare this page
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.