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Author Triebel, Hans, author
Title Local function spaces, heat and Navier-Stokes equations / Hans Triebel
Imprint Zürich, Switzerland : European Mathematical Society Publishing House, [2013]
book jacket
 Mathematics Library  QA323 T7524 2013    AVAILABLE    30340200532376
Descript ix, 232 pages : illustration ; 25 cm
text rdacontent
unmediated rdamedia
volume rdacarrier
Series EMS tracts in mathematics ; 20
EMS tracts in mathematics ; 20
Note Includes bibliographical references (pages 215-227) and index
1. Global and local spaces -- 2. Local spaces: properties -- 3. Morrey-Campanato spaces -- 4. Galiardo-Nirenberg inequalities -- 5. Heat equations -- 6, Navier-Stokes equations
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
Subject Function spaces
Heat equation
Navier-Stokes equations
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