Global Regularity For 2d Water Waves With Surface Tension
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Global Regularity For 2d Water Waves With Surface Tension
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Author : Alexandru D. Ionescu
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-01-08
Global Regularity For 2d Water Waves With Surface Tension written by Alexandru D. Ionescu and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-01-08 with Capillarity categories.
The authors consider the full irrotational water waves system with surface tension and no gravity in dimension two (the capillary waves system), and prove global regularity and modified scattering for suitably small and localized perturbations of a flat interface. An important point of the authors' analysis is to develop a sufficiently robust method (the “quasilinear I-method”) which allows the authors to deal with strong singularities arising from time resonances in the applications of the normal form method (the so-called “division problem”). As a result, they are able to consider a suitable class of perturbations with finite energy, but no other momentum conditions. Part of the authors' analysis relies on a new treatment of the Dirichlet-Neumann operator in dimension two which is of independent interest. As a consequence, the results in this paper are self-contained.
Angled Crested Like Water Waves With Surface Tension Ii Zero Surface Tension Limit
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Author : Siddhant Agrawal
language : en
Publisher: American Mathematical Society
Release Date : 2024-02-01
Angled Crested Like Water Waves With Surface Tension Ii Zero Surface Tension Limit written by Siddhant Agrawal and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-02-01 with Mathematics categories.
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Almost Global Solutions Of Capillary Gravity Water Waves Equations On The Circle
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Author : Massimiliano Berti
language : en
Publisher: Springer
Release Date : 2018-11-02
Almost Global Solutions Of Capillary Gravity Water Waves Equations On The Circle written by Massimiliano Berti and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-02 with Mathematics categories.
The goal of this monograph is to prove that any solution of the Cauchy problem for the capillary-gravity water waves equations, in one space dimension, with periodic, even in space, small and smooth enough initial data, is almost globally defined in time on Sobolev spaces, provided the gravity-capillarity parameters are taken outside an exceptional subset of zero measure. In contrast to the many results known for these equations on the real line, with decaying Cauchy data, one cannot make use of dispersive properties of the linear flow. Instead, a normal forms-based procedure is used, eliminating those contributions to the Sobolev energy that are of lower degree of homogeneity in the solution. Since the water waves equations form a quasi-linear system, the usual normal forms approaches would face the well-known problem of losses of derivatives in the unbounded transformations. To overcome this, after a paralinearization of the capillary-gravity water waves equations, we perform several paradifferential reductions to obtain a diagonal system with constant coefficient symbols, up to smoothing remainders. Then we start with a normal form procedure where the small divisors are compensated by the previous paradifferential regularization. The reversible structure of the water waves equations, and the fact that we seek solutions even in space, guarantees a key cancellation which prevents the growth of the Sobolev norms of the solutions.
Introduction To Water Waves
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Author : Gordon David Crapper
language : en
Publisher:
Release Date : 1984
Introduction To Water Waves written by Gordon David Crapper and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with Water waves categories.
Lectures On The Theory Of Water Waves
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Author : Thomas J. Bridges
language : en
Publisher: Cambridge University Press
Release Date : 2016-02-04
Lectures On The Theory Of Water Waves written by Thomas J. Bridges and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-02-04 with Mathematics categories.
A range of experts contribute introductory-level lectures on active topics in the theory of water waves.
Quasi Periodic Standing Wave Solutions Of Gravity Capillary Water Waves
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Author : Massimiliano Berti
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-04-03
Quasi Periodic Standing Wave Solutions Of Gravity Capillary Water Waves written by Massimiliano Berti and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-04-03 with Education categories.
The authors prove the existence and the linear stability of small amplitude time quasi-periodic standing wave solutions (i.e. periodic and even in the space variable x) of a 2-dimensional ocean with infinite depth under the action of gravity and surface tension. Such an existence result is obtained for all the values of the surface tension belonging to a Borel set of asymptotically full Lebesgue measure.
Quiver Grassmannians Of Extended Dynkin Type D Part I Schubert Systems And Decompositions Into Affine Spaces
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Author : Oliver Lorscheid
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-12-02
Quiver Grassmannians Of Extended Dynkin Type D Part I Schubert Systems And Decompositions Into Affine Spaces written by Oliver Lorscheid and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-12-02 with Education categories.
Let Q be a quiver of extended Dynkin type D˜n. In this first of two papers, the authors show that the quiver Grassmannian Gre–(M) has a decomposition into affine spaces for every dimension vector e– and every indecomposable representation M of defect −1 and defect 0, with the exception of the non-Schurian representations in homogeneous tubes. The authors characterize the affine spaces in terms of the combinatorics of a fixed coefficient quiver for M. The method of proof is to exhibit explicit equations for the Schubert cells of Gre–(M) and to solve this system of equations successively in linear terms. This leads to an intricate combinatorial problem, for whose solution the authors develop the theory of Schubert systems. In Part 2 of this pair of papers, they extend the result of this paper to all indecomposable representations M of Q and determine explicit formulae for the F-polynomial of M.
One Dimensional Empirical Measures Order Statistics And Kantorovich Transport Distances
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Author : Sergey Bobkov
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-12-02
One Dimensional Empirical Measures Order Statistics And Kantorovich Transport Distances written by Sergey Bobkov and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-12-02 with Education categories.
This work is devoted to the study of rates of convergence of the empirical measures μn=1n∑nk=1δXk, n≥1, over a sample (Xk)k≥1 of independent identically distributed real-valued random variables towards the common distribution μ in Kantorovich transport distances Wp. The focus is on finite range bounds on the expected Kantorovich distances E(Wp(μn,μ)) or [E(Wpp(μn,μ))]1/p in terms of moments and analytic conditions on the measure μ and its distribution function. The study describes a variety of rates, from the standard one 1n√ to slower rates, and both lower and upper-bounds on E(Wp(μn,μ)) for fixed n in various instances. Order statistics, reduction to uniform samples and analysis of beta distributions, inverse distribution functions, log-concavity are main tools in the investigation. Two detailed appendices collect classical and some new facts on inverse distribution functions and beta distributions and their densities necessary to the investigation.
Automorphisms Oftwo Generator Free Groups And Spaces Of Isometric Actions On The Hyperbolic Plane
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Author : William Goldman
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-06-10
Automorphisms Oftwo Generator Free Groups And Spaces Of Isometric Actions On The Hyperbolic Plane written by William Goldman and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-06-10 with Automorphisms categories.
The automorphisms of a two-generator free group F acting on the space of orientation-preserving isometric actions of F on hyperbolic 3-space defines a dynamical system. Those actions which preserve a hyperbolic plane but not an orientation on that plane is an invariant subsystem, which reduces to an action of a group on by polynomial automorphisms preserving the cubic polynomial and an area form on the level surfaces .
Fusion Of Defects
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Author : Arthur Bartels
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-04-10
Fusion Of Defects written by Arthur Bartels and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-04-10 with Generalized spaces categories.
Conformal nets provide a mathematical model for conformal field theory. The authors define a notion of defect between conformal nets, formalizing the idea of an interaction between two conformal field theories. They introduce an operation of fusion of defects, and prove that the fusion of two defects is again a defect, provided the fusion occurs over a conformal net of finite index. There is a notion of sector (or bimodule) between two defects, and operations of horizontal and vertical fusion of such sectors. The authors' most difficult technical result is that the horizontal fusion of the vacuum sectors of two defects is isomorphic to the vacuum sector of the fused defect. Equipped with this isomorphism, they construct the basic interchange isomorphism between the horizontal fusion of two vertical fusions and the vertical fusion of two horizontal fusions of sectors.