Shocks, singularities and oscillations in nonlinear optics and fluid mechanics. (2017)

• Record Type: Book
• Further Information: Note: Ferruccio Colombini, Daniele Del Santo, David Lannes, editors.
• Editors: Colombini, F (Ferruccio); Del Santo, Daniele; Lannes, David, 1973-
• Contents: Preface; Contents; Contributors; Amplitude Equations for Weakly Nonlinear Surface Wavesin Variational Problems; 1 Introduction; 2 Amplitude Equations in Abstract Variational Problems; 2.1 General Framework; 2.2 Linear Surface Waves; 2.3 Weakly Nonlinear Asymptotics; 2.4 Derivation of Amplitude Equations; 2.5 Well-Posedness Theory of Amplitude Equations; 3 Surface Waves at Reversible Phase Boundaries; 3.1 Phase Boundaries Versus Classical Shocks; 3.2 Glimpse of the Amplitude Equation; 3.3 Linear Surface Waves; 3.4 Well-Posedness of the Amplitude Equation; Appendix; References. Global Weak Solutions of PDEs for Compressible Media:A Compactness Criterion to Cover New Physical Situations1 Introduction; 2 Equations and Main Result; 2.1 Statements of the Result; 3 Sketch of the New Compactness Method; 3.1 The Compactness Criterion; 4 Proof of Theorem 2.1; 4.1 Energy Estimates and Control of Unknowns; 4.2 Stability of Weak Sequences: Compactness; 4.3 Construction of Approximate Solutions; 5 The Compressible Navier-Stokes Equations; Appendix; References; Second Microlocalization and Stabilization of Damped Wave Equations on Tori; 1 Notations and Main Results. 2 Resolvent Estimates and Stabilization2.1 Resolvent Estimates and Stabilization; 2.2 Resolvent Estimates and Damped Wave Equations; 2.2.1 Semi-groups for Damped Wave Equations; 2.2.2 Reduction to High Frequency Observation Estimates; 3 The Model Case of a Checkerboard; 3.1 First Micro-localization; 3.2 A Priori Non Concentration Estimate; 3.3 Second Micro-localization; 3.3.1 Symbols and Operators; 3.3.2 Definition of the Second Semi-classical Measures; 3.3.3 Properties of the Second Semi-classical Measure; 4 Assumption 1.6 is Necessary: A Sketch of the Proof; References. A Few Remarks on Hyperbolic Systems with Zygmundin Time Coefficients1 Introduction; 1.1 Motivations; 1.2 Background: A Quick Overview; 1.3 Contents of the Paper; 1.3.1 Structure of the Paper; 1.3.2 Notations; 2 The Main Result; 2.1 Basic Definitions and Hypotheses; 2.2 Finite Speed of Propagation; 3 Well-Posedness in Sobolev Classes; 3.1 The Basic Energy Estimate; 3.2 Some Remarks; 3.3 Sketch of the Proof; 3.3.1 Approximation Scheme; 3.3.2 Construction of the Approximate Symmetrizer; 3.3.3 Energy Estimates; 3.4 The Global in Time Estimate; 4 Proof of the Finite Propagation Speed Property. 4.1 A Key Estimate4.1.1 High Frequencies Estimates; 4.1.2 Low Frequencies Estimate; 4.2 End of the Proof of Theorem 2.6; References; Wellposedness of Linearized Taylor Equationsin Magnetohydrodynamics; 1 Presentation of the Model and Main Result; 1.1 Introduction; 1.2 The Taylor Model; 1.3 The Taylor Model in the Torus; 1.4 Linearization and Statement of the Main Result; 2 Preliminaries and Reductions; 2.1 Computation of the Linear Taylor Constraint and the Magnetostrophic Field; 2.2 Computation of the Geostrophic Field; 2.3 Fourier Transform; 2.4 Reduction to Large Horizontal Frequencies.
• Publisher Details: Cham, Switzerland : Springer
• Publication Date: 2017
• Extent: 1 online resource (xii, 308 pages), illustrations (some color)
• Subjects: 515/.3535; 510; Mathematics; Exponential functions; Nonlinear systems; MATHEMATICS -- Calculus; MATHEMATICS -- Mathematical Analysis; Exponential functions; Nonlinear systems; Mathematics; Partial Differential Equations; Fourier Analysis; Mathematical Physics; Applications of Mathematics; Science -- Mathematical Physics; Mathematics -- Applied; Functional analysis & transforms; Mathematical physics; Applied mathematics; Differential equations, partial; Fourier analysis; Mathematics -- Differential Equations; Differential calculus & equations; Electronic books
• Languages: English
• ISBNs: 9783319520421; 3319520423
• Related ISBNs: 9783319520414; 3319520415
• Notes: Note: Includes bibliographical references at the end of each chapters.; Note: Online resource; title from PDF title page (SpringerLink, viewed May 5, 2017).
• 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.