Download or read book Almost Global Solutions of Capillary Gravity Water Waves Equations on the Circle written by Massimiliano Berti and published by Springer. This book was released on 2018-11-02 with total page 269 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Waves in Flows written by Tomáš Bodnár and published by Springer Nature. This book was released on 2021-04-29 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Free Boundary Problems in Fluid Dynamics written by Albert Ai and published by Springer Nature. This book was released on with total page 373 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Quasi Periodic Traveling Waves on an Infinitely Deep Perfect Fluid Under Gravity written by Roberto Feola and published by American Mathematical Society. This book was released on 2024-04-17 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.
Download or read book Quasi periodic Standing Wave Solutions of Gravity capillary Water Waves written by Massimiliano Berti and published by . This book was released on 2020 with total page 171 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Solitons written by Mohamed Atef Helal and published by Springer Nature. This book was released on 2022-11-12 with total page 483 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Introduction to Water Waves written by Gordon David Crapper and published by . This book was released on 1984 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Philosophical Transactions of the Royal Society written by and published by . This book was released on 2007 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1983 with total page 1252 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Satellite Altimetry and Earth Sciences written by Lee-Lueng Fu and published by Elsevier. This book was released on 2000-11-09 with total page 463 pages. Available in PDF, EPUB and Kindle. Book excerpt: The new level of precision and global coverage provided by satellite altimetry is rapidly advancing studies of ocean circulation. It allows for new insights into marine geodesy, ice sheet movements, plate tectonics, and for the first time provides high-resolution bathymetry for previously unmapped regions of our watery planet and crucial information on the large-scale ocean features on intra-season to interannual time scales. Satellite Altimetry and Earth Sciences has integrated the expertise of the leading international researchers to demonstrate the techniques, missions, and accuracy of satellite altimetry, including altimeter measurements, orbit determination, and ocean circulation models. Satellite altimetry is helping to advance studies of ocean circulation, tides, sea level, surface waves and allowing new insights into marine geodesy. Satellite Altimetry and Earth Sciences provides high resolution bathymetry for previously unmapped regions of our watery planet. Satellite Altimetry and Earth Sciences is for a very broad spectrum of academics, graduate students, and researchers in geophysics, oceanography, and the space and earth sciences. International agencies that fund satellite-based research will also appreciate the handy reference on the applications of satellite altimetry.
Download or read book Global Regularity for 2D Water Waves with Surface Tension written by Alexandru Dan Ionescu and published by . This book was released on 2018 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Mathematical Reviews written by and published by . This book was released on 2005 with total page 1852 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Interaction of Ocean Waves and Wind written by Peter Janssen and published by Cambridge University Press. This book was released on 2004-10-28 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Proceedings of the International Symposium written by Michael Isaacson and published by . This book was released on 1994 with total page 582 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Special Report Corps of Engineers U S Army Cold Regions Research and Engineering Laboratory written by Cold Regions Research and Engineering Laboratory (U.S.) and published by . This book was released on 1972 with total page 478 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Energy Research Abstracts written by and published by . This book was released on 1979 with total page 1038 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Global Nonlinear Stability of the Minkowski Space PMS 41 written by Demetrios Christodoulou and published by Princeton University Press. This book was released on 2014-07-14 with total page 525 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
