Strichartz Estimates And The Cauchy Problem For The Gravity Water Waves Equations
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Strichartz Estimates And The Cauchy Problem For The Gravity Water Waves Equations
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Author : T. Alazard
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-01-08
Strichartz Estimates And The Cauchy Problem For The Gravity Water Waves Equations written by T. Alazard 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 Mathematics categories.
This memoir is 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. Moreover, for two-dimensional waves, the authors consider solutions such that the curvature of the initial free surface does not belong to L2. The proof is entirely based on the Eulerian formulation of the water waves equations, using microlocal analysis to obtain sharp Sobolev and Hölder estimates. The authors first prove tame estimates in Sobolev spaces depending linearly on Hölder norms and then use the dispersive properties of the water-waves system, namely Strichartz estimates, to control these Hölder norms.
Free Boundary Problems In Fluid Dynamics
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Author : Albert Ai
language : en
Publisher: Springer Nature
Release Date : 2024-06-18
Free Boundary Problems In Fluid Dynamics written by Albert Ai and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-06-18 with Mathematics categories.
This book, originating from a seminar held at Oberwolfach in 2022, introduces to state-of-the-art methods and results in the study of free boundary problems which are arising from compressible as well as from incompressible Euler’s equations in general. A particular set of such problems is given by gaseous stars considered in a vacuum (modeled via the compressible Euler equations) as well as water waves in their full generality (seen as recasts of incompressible irrotational Euler equations). This is a broad research area which is highly relevant to many real life problems, and in which substantial progress has been made in the last decade.
Mathematics Of Wave Phenomena
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Author : Willy Dörfler
language : en
Publisher: Springer Nature
Release Date : 2020-10-01
Mathematics Of Wave Phenomena written by Willy Dörfler and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-01 with Mathematics categories.
Wave phenomena are ubiquitous in nature. Their mathematical modeling, simulation and analysis lead to fascinating and challenging problems in both analysis and numerical mathematics. These challenges and their impact on significant applications have inspired major results and methods about wave-type equations in both fields of mathematics. The Conference on Mathematics of Wave Phenomena 2018 held in Karlsruhe, Germany, was devoted to these topics and attracted internationally renowned experts from a broad range of fields. These conference proceedings present new ideas, results, and techniques from this exciting research area.
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.
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.
View the abstract.
Local Well Posedness And Break Down Criterion Of The Incompressible Euler Equations With Free Boundary
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Author : Chao Wang
language : en
Publisher: American Mathematical Soc.
Release Date : 2021-07-21
Local Well Posedness And Break Down Criterion Of The Incompressible Euler Equations With Free Boundary written by Chao Wang 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 2021-07-21 with Education categories.
In this paper, we prove the local well-posedness of the free boundary problem for the incompressible Euler equations in low regularity Sobolev spaces, in which the velocity is a Lipschitz function and the free surface belongs to C 3 2 +ε. Moreover, we also present a Beale-Kato-Majda type break-down criterion of smooth solution in terms of the mean curvature of the free surface, the gradient of the velocity and Taylor sign condition.
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 Mathematics 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.
Time Changes Of The Brownian Motion Poincar Inequality Heat Kernel Estimate And Protodistance
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Author : Jun Kigami
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-06-10
Time Changes Of The Brownian Motion Poincar Inequality Heat Kernel Estimate And Protodistance written by Jun Kigami 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 Mathematics categories.
In this paper, time changes of the Brownian motions on generalized Sierpinski carpets including n-dimensional cube [0,1]n are studied. Intuitively time change corresponds to alteration to density of the medium where the heat flows. In case of the Brownian motion on [0,1]n, density of the medium is homogeneous and represented by the Lebesgue measure. The author's study includes densities which are singular to the homogeneous one. He establishes a rich class of measures called measures having weak exponential decay. This class contains measures which are singular to the homogeneous one such as Liouville measures on [0,1]2 and self-similar measures. The author shows the existence of time changed process and associated jointly continuous heat kernel for this class of measures. Furthermore, he obtains diagonal lower and upper estimates of the heat kernel as time tends to 0. In particular, to express the principal part of the lower diagonal heat kernel estimate, he introduces “protodistance” associated with the density as a substitute of ordinary metric. If the density has the volume doubling property with respect to the Euclidean metric, the protodistance is shown to produce metrics under which upper off-diagonal sub-Gaussian heat kernel estimate and lower near diagonal heat kernel estimate will be shown.
On Space Time Quasiconcave Solutions Of The Heat Equation
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Author : Chuanqiang Chen
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-06-10
On Space Time Quasiconcave Solutions Of The Heat Equation written by Chuanqiang Chen 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 Mathematics categories.
In this paper the authors first obtain a constant rank theorem for the second fundamental form of the space-time level sets of a space-time quasiconcave solution of the heat equation. Utilizing this constant rank theorem, they obtain some strictly convexity results of the spatial and space-time level sets of the space-time quasiconcave solution of the heat equation in a convex ring. To explain their ideas and for completeness, the authors also review the constant rank theorem technique for the space-time Hessian of space-time convex solution of heat equation and for the second fundamental form of the convex level sets for harmonic function.
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.