Local function spaces, heat and Navier-Stokes equations / Hans Triebel
- Triebel, Hans
- Zürich, Switzerland : European Mathematical Society Publishing House, 
- Copyright Date:
- Physical Description:
- ix, 232 pages : illustration ; 25 cm.
- EMS tracts in mathematics ; 20
- 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.
- Bibliography Note:
- Includes bibliographical references (pages -227) and index.
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