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Strichartz Estimates and the Cauchy Problem for the Gravity Water Waves Equations
This memoir is devoted to the proof of a well-posedness result for the gravity water waves equations, in arbitrary dimension and in fluid domains with general bottoms, when the initial velocity field is not necessarily Lipschitz. Moreover, for two-dimensional waves, the authors consider solutions su...
| Cote: | Libro Electrónico |
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| Auteur principal: | |
| Autres auteurs: | , |
| Format: | Électronique eBook |
| Langue: | Inglés |
| Publié: |
Providence :
American Mathematical Society,
2019.
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| Collection: | Memoirs of the American Mathematical Society Ser.
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| Sujets: | |
| Accès en ligne: | Texto completo |
Table des matières:
- Cover; Title page; Chapter 1. Introduction; 1.1. Equations and assumptions on the fluid domain; 1.2. Regularity thresholds for the water waves; 1.3. Reformulation of the equations; 1.4. Main result; 1.5. Paradifferential reduction; 1.6. Strichartz estimates; Chapter 2. Strichartz estimates; 2.1. Symmetrization of the equations; 2.2. Smoothing the paradifferential symbol; 2.3. The pseudo-differential symbol; 2.4. Several reductions; 2.5. Straightening the vector field; 2.6. Reduction to a semi-classical form; 2.7. The parametrix; 2.8. The dispersion estimate; 2.9. The Strichartz estimates
- Chapter 3. Cauchy problem3.1. A priori estimates; 3.2. Contraction estimates; 3.3. Passing to the limit in the equations; 3.4. Existence and uniqueness; Appendix A. Paradifferential calculus; A.1. Notations and classical results; A.2. Symbolic calculus; A.3. Paraproducts and product rules; Appendix B. Tame estimates for the Dirichlet-Neumann operator; B.1. Scheme of the analysis; B.2. Parabolic evolution equation; B.3. Paralinearization; Appendix C. Estimates for the Taylor coefficient; Appendix D. Sobolev estimates; D.1. Introduction; D.2. Symmetrization of the equations
- D.3. Sobolev estimatesAppendix E. Proof of a technical result; Bibliography; Back Cover