Almost Global Solutions Of Capillary Gravity Water Waves Equations On The Circle
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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.
Waves In Flows
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Author : Tomáš Bodnár
language : en
Publisher: Springer Nature
Release Date : 2021-04-29
Waves In Flows written by Tomáš Bodnár and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-04-29 with Mathematics categories.
This volume offers an overview of the area of waves in fluids and the role they play in the mathematical analysis and numerical simulation of fluid flows. Based on lectures given at the summer school “Waves in Flows”, held in Prague from August 27-31, 2018, chapters are written by renowned experts in their respective fields. Featuring an accessible and flexible presentation, readers will be motivated to broaden their perspectives on the interconnectedness of mathematics and physics. A wide range of topics are presented, working from mathematical modelling to environmental, biomedical, and industrial applications. Specific topics covered include: Equatorial wave–current interactions Water–wave problems Gravity wave propagation Flow–acoustic interactions Waves in Flows will appeal to graduate students and researchers in both mathematics and physics. Because of the applications presented, it will also be of interest to engineers working on environmental and industrial issues.
Quasi Periodic Traveling Waves On An Infinitely Deep Perfect Fluid Under Gravity
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Author : Roberto Feola
language : en
Publisher: American Mathematical Society
Release Date : 2024-04-17
Quasi Periodic Traveling Waves On An Infinitely Deep Perfect Fluid Under Gravity written by Roberto Feola 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 2024-04-17 with Mathematics categories.
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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.
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.
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.
Solitons
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Author : Mohamed Atef Helal
language : en
Publisher: Springer Nature
Release Date : 2022-11-12
Solitons written by Mohamed Atef Helal and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-11-12 with Science categories.
This newly updated volume of the Encyclopedia of Complexity and Systems Science (ECSS) presents several mathematical models that describe this physical phenomenon, including the famous non-linear equation Korteweg-de-Vries (KdV) that represents the canonical form of solitons. Also, there exists a class of nonlinear partial differential equations that led to solitons, e.g., Kadomtsev-Petviashvili (KP), Klein-Gordon (KG), Sine-Gordon (SG), Non-Linear Schrödinger (NLS), Korteweg-de-Vries Burger’s (KdVB), etc. Different linear mathematical methods can be used to solve these models analytically, such as the Inverse Scattering Transformation (IST), Adomian Decomposition Method, Variational Iteration Method (VIM), Homotopy Analysis Method (HAM) and Homotopy Perturbation Method (HPM). Other non-analytic methods use the computational techniques available in such popular mathematical packages as Mathematica, Maple, and MATLAB. The main purpose of this volume is to provide physicists, engineers, and their students with the proper methods and tools to solve the soliton equations, and to discover the new possibilities of using solitons in multi-disciplinary areas ranging from telecommunications to biology, cosmology, and oceanographic studies.
The Global Nonlinear Stability Of The Minkowski Space Pms 41
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Author : Demetrios Christodoulou
language : en
Publisher: Princeton University Press
Release Date : 2014-07-14
The Global Nonlinear Stability Of The Minkowski Space Pms 41 written by Demetrios Christodoulou and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-14 with Mathematics categories.
The aim of this work is to provide a proof of the nonlinear gravitational stability of the Minkowski space-time. More precisely, the book offers a constructive proof of global, smooth solutions to the Einstein Vacuum Equations, which look, in the large, like the Minkowski space-time. In particular, these solutions are free of black holes and singularities. The work contains a detailed description of the sense in which these solutions are close to the Minkowski space-time, in all directions. It thus provides the mathematical framework in which we can give a rigorous derivation of the laws of gravitation proposed by Bondi. Moreover, it establishes other important conclusions concerning the nonlinear character of gravitational radiation. The authors obtain their solutions as dynamic developments of all initial data sets, which are close, in a precise manner, to the flat initial data set corresponding to the Minkowski space-time. They thus establish the global dynamic stability of the latter. Originally published in 1994. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Philosophical Transactions Of The Royal Society
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Author :
language : en
Publisher:
Release Date : 2007
Philosophical Transactions Of The Royal Society written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Engineering categories.
The Interaction Of Ocean Waves And Wind
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Author : Peter Janssen
language : en
Publisher: Cambridge University Press
Release Date : 2004-10-28
The Interaction Of Ocean Waves And Wind written by Peter Janssen 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 2004-10-28 with Science categories.
This book was published in 2004. The Interaction of Ocean Waves and Wind describes in detail the two-way interaction between wind and ocean waves and shows how ocean waves affect weather forecasting on timescales of 5 to 90 days. Winds generate ocean waves, but at the same time airflow is modified due to the loss of energy and momentum to the waves; thus, momentum loss from the atmosphere to the ocean depends on the state of the waves. This volume discusses ocean wave evolution according to the energy balance equation. An extensive overview of nonlinear transfer is given, and as a by-product the role of four-wave interactions in the generation of extreme events, such as freak waves, is discussed. Effects on ocean circulation are described. Coupled ocean-wave, atmosphere modelling gives improved weather and wave forecasts. This volume will interest ocean wave modellers, physicists and applied mathematicians, and engineers interested in shipping and coastal protection.