Local Function Spaces, Heat and Navier-Stokes Equations
Triebel H.
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 -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
Categorias:
Ano:
2013
Editora:
European Mathematical Society
Idioma:
english
Páginas:
242
ISBN 10:
3037191236
ISBN 13:
9783037191231
Série:
EMS Tracts in Mathematics
Arquivo:
PDF, 1.25 MB
IPFS:
,
english, 2013