Almost global solutions of capillary-gravity water waves equations on the circle. (2018)

• Record Type: Book
• Further Information: Note: Massimiliano Berti, Jean-Marc Delort.
• Authors: Berti, Massimiliano; Delort, Jean-Marc, 1961-
• Contents: Introduction.-Main Theorem.-Introduction to the proof.- Paradifferential formulation.-Reduction to constant coefficients.-Normal forms.-Main result.-The periodic capillarity-gravity equations .-Statement of the main theorem.-Paradifferential calculus.-Classes of symbols.-Quantization of symbols.-Symbolic calculus.-Composition theorems.-Paracomposition.-Complex equations and diagonalization.-Reality, parity and reversibility properties.-Complex formulation.-Diagonalization of the system.-Reductions and proof of main theorem.-Reduction of highest order.-Reduction to constant coefficient symbols.-Normal forms.-Proof of Theorem.-Dirichlet-Neumann problem.-Paradifferential and para-Poisson operators.-Parametrix of Dirichlet-Neumann problem.-Solving the Dirichlet-Neumann problem.-Dirichlet-Neumann and good unknown.-The good unknown.-Paralinearization of the system.-Equation in complex coordinates.-Proof of some auxiliary results.-Non resonance condition.-Structure of Dirichlet-Neumann operator.-References.-Index.
• Publisher Details: Cham, Switzerland : Springer
• Publication Date: 2018
• Extent: 1 online resource (x, 269 pages), illustrations
• Subjects: 515/.35; Mathematics; Cauchy problem; Sobolev spaces; Mathematics -- Mathematical Analysis; Mathematics -- Functional Analysis; Functional analysis & transforms; Nonlinear science; Differential equations, partial; Fourier analysis; Differentiable dynamical systems; Functional analysis; Mathematics -- Differential Equations; Differential calculus & equations; Electronic books
• Languages: English
• ISBNs: 9783319994864; 3319994867
• Related ISBNs: 9783319994857
• Notes: Note: Includes bibliographical references and index.; Note: Online resource; title from PDF title page (SpringerLink, viewed November 12, 2018).
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.