Small Divisor Problem in the Theory of Three-Dimensional Water Gravity Waves.

Intro -- Contents -- Chapter 1. Introduction -- 1.1. Presentation and History of the Problem -- 1.2. Formulation of the Problem -- 1.3. Results -- 1.4. Mathematical background -- 1.5. Structure of the paper -- Chapter 2. Formal Solutions -- 2.1. Differential of G[sub(n)] -- 2.2. Linearized equations at the origin and dispersion relation -- 2.3. Formal computation of 3-dimensional waves -- 2.4. Geometric pattern of diamond waves -- Chapter 3. Linearized Operator -- 3.1. Linearized system in (ψ,n) ≠ 0 -- 3.2. Pseudodifferential operators and diffeomorphism of the torus -- 3.3. Main orders of the diffeomorphism and coefficient v -- Chapter 4. Small Divisors. Estimate of L - Resolvent -- 4.1. Proof of Theorem 4.10 -- Chapter 5. Descent Method-Inversion of the Linearized Operator -- 5.1. Descent method -- 5.2. Proof of Theorem 5.1 -- 5.3. Verification of assumptions of Theorem 5.1 -- 5.4. Inversion of L -- Chapter 6. Nonlinear Problem. Proof of Theorem 1.3 -- Appendix A. Analytical study of G[sub(n)] -- A.1. Computation of the differential of G[sub(n)] -- A.2. Second order Taylor expansion of G[sub(n)] in n = 0 -- Appendix B. Formal computation of 3-dimensional waves -- B.1. Formal Fredholm alternative -- B.2. Bifurcation equation -- Appendix C. Proof of Lemma 3.6 -- Appendix D. Proofs of Lemmas 3.7 and 3.8 -- Appendix E. Distribution of Numbers {ω[sub(0)]n[sup(2)]} -- Appendix F. Pseudodifferential Operators -- Appendix G. Dirichlet-Neumann Operator -- Appendix H. Proof of Lemma 5.8 -- Appendix I. Fluid particles dynamics -- Bibliography.

Description based on publisher supplied metadata and other sources.

Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.