Almost Global Solutions of Capillary-Gravity Water Waves Equations on the Circle - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Almost Global Solutions of Capillary-Gravity Water Waves Equations on the Circle write by Massimiliano Berti. This book was released on 2018-11-02. Almost Global Solutions of Capillary-Gravity Water Waves Equations on the Circle available in PDF, EPUB and Kindle. 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.
Quasi-Periodic Traveling Waves on an Infinitely Deep Perfect Fluid Under Gravity
Quasi-Periodic Traveling Waves on an Infinitely Deep Perfect Fluid Under Gravity - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Quasi-Periodic Traveling Waves on an Infinitely Deep Perfect Fluid Under Gravity write by Roberto Feola. This book was released on 2024-04-17. Quasi-Periodic Traveling Waves on an Infinitely Deep Perfect Fluid Under Gravity available in PDF, EPUB and Kindle. View the abstract.
Waves in Flows
Waves in Flows - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Waves in Flows write by Tomáš Bodnár. This book was released on 2021-04-29. Waves in Flows available in PDF, EPUB and Kindle. 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.
Free Boundary Problems in Fluid Dynamics
Free Boundary Problems in Fluid Dynamics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Free Boundary Problems in Fluid Dynamics write by Albert Ai. This book was released on . Free Boundary Problems in Fluid Dynamics available in PDF, EPUB and Kindle.
Nonlinear Water Waves
Nonlinear Water Waves - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Nonlinear Water Waves write by David Henry. This book was released on 2019-11-27. Nonlinear Water Waves available in PDF, EPUB and Kindle. The motion of water is governed by a set of mathematical equations which are extremely complicated and intractable. This is not surprising when one considers the highly diverse and intricate physical phenomena which may be exhibited by a given body of water. Recent mathematical advances have enabled researchers to make major progress in this field, reflected in the topics featured in this volume. Cutting-edge techniques and tools from mathematical analysis have generated strong rigorous results concerning the qualitative and quantitative physical properties of solutions of the governing equations. Furthermore, accurate numerical computations of fully-nonlinear steady and unsteady water waves in two and three dimensions have contributed to the discovery of new types of waves. Model equations have been derived in the long-wave and modulational regime using Hamiltonian formulations and solved numerically. This book brings together interdisciplinary researchers working in the field of nonlinear water waves, whose contributions range from survey articles to new research results which address a variety of aspects in nonlinear water waves. It is motivated by a workshop which was organised at the Erwin Schrödinger International Institute for Mathematics and Physics in Vienna, November 27-December 7, 2017. The key aim of the workshop was to describe, and foster, new approaches to research in this field. This is reflected in the contents of this book, which is aimed to stimulate both experienced researchers and students alike.
