Almost Global Solutions of Capillary-Gravity Water Waves Equations on the Circle, Massimiliano Berti; Jean-Marc Delort

Автор: Massimiliano Berti, Riccardo Montalto
Название: Quasi-periodic Standing Wave Solutions of Gravity-Capillary Water Waves
ISBN: 1470440695 ISBN-13(EAN): 9781470440695
Издательство: Mare Nostrum (Eurospan)
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Цена: 71060.00 T
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Описание: 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.

Автор: Marko Kostic
Название: Almost Periodic and Almost Automorphic Solutions to Integro-Differential Equations
ISBN: 3110641240 ISBN-13(EAN): 9783110641240
Издательство: Walter de Gruyter
Цена: 140030.00 T
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Описание: This book discusses almost periodic and almost automorphic solutions to abstract integro-differential Volterra equations that are degenerate in time, and in particular equations whose solutions are governed by (degenerate) solution operator families with removable singularities at zero. It particularly covers abstract fractional equations and inclusions with multivalued linear operators as well as abstract fractional semilinear Cauchy problems.

Автор: T. Alazard, N. Burq, C. Zuily
Название: Strichartz Estimates and the Cauchy Problem for the Gravity Water Waves Equations
ISBN: 147043203X ISBN-13(EAN): 9781470432034
Издательство: Mare Nostrum (Eurospan)
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Цена: 80390.00 T
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Описание: Devoted to the proof of a well-posedness result for the gravity water waves equations, in arbitrary dimension and in fluid domains with general bottoms, when the initial velocity field is not necessarily Lipschitz. For two-dimensional waves, the authors consider solutions such that the curvature of the initial free surface does not belong to $L^2$.

Автор: Alexandru D. Ionescu, Fabio Pusateri
Название: Global Regularity for 2D Water Waves with Surface Tension
ISBN: 1470431033 ISBN-13(EAN): 9781470431037
Издательство: Mare Nostrum (Eurospan)
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Цена: 65210.00 T
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Описание: 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.

Название: Global Solutions And The Asymptotic Behavior For Nonlinear Wave Equations With Small Initial Data
ISBN: 4864970548 ISBN-13(EAN): 9784864970549
Издательство: World Scientific Publishing
Цена: 44350.00 T
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Описание: In the study of the Cauchy problem for nonlinear wave equations with small initial data, the case where the nonlinearity has the critical power is of special interest. In this case, depending on the structure of the nonlinearity, one may observe global existence and finite time blow-up of solutions. In 80's, Klainerman introduced a sufficient condition, called the null condition, for the small data global existence in the critical case. Recently, weaker sufficient conditions are also studied.This volume offers a comprehensive survey of the theory of nonlinear wave equations, including the classical local existence theorem, the global existence in the supercritical case, the finite time blow-up and the lifespan estimate in the critical case, and the global existence under the null condition in two and three space dimensions. The main tool here is the so-called vector field method. This volume also contains recent progress in the small data global existence under some conditions weaker than the null condition, and it is shown that a wide variety of the asymptotic behavior is observed under such weaker conditions.This volume is written not only for researchers, but also for graduate students who are interested in nonlinear wave equations. The exposition is intended to be self-contained and a complete proof is given for each theorem.Published by Mathematical Society of Japan and distributed by World Scientific Publishing Co. for all markets