Strichartz estimates and the Cauchy prob
β Alazard T
π Library
π
2018
π American Mathematical Society
π English
β¦ LIBER β¦
π
Sobolev Estimates for Two Dimensional Gravity Water Waves
β Scribed by Thomas Alazard, Jean-Marc Delort
- Publisher
- Societe Mathematique De France
- Year
- 2015
- Tongue
- English
- Leaves
- 254
- Series
- Asterisque 374
- Category
- Library
β¬ Acquire This Volume
No coin nor oath required. For personal study only.
β¦ Synopsis
Our goal in this volume is to apply a normal forms method to estimate the Sobolev norms of the solutions of the water waves equation. We construct a paradifferential change of unknown, without derivatives losses, which eliminates the part of the quadratic terms that bring non zero contributions in a Sobolev energy inequality. Our approach is purely Eulerian: we work on the Craig-Sulem-Zakharov formulation of the water waves equation. In addition to these Sobolev estimates, we also prove L^2-estimates for the ^Z^-derivatives of the solutions of the water waves equation, where Z is the Klainerman vector field t_t +2x. These estimates are used in the paper [6]. In that reference, we prove a global existence result for the water waves equation with smooth, small, and decaying at infinity Cauchy data, and we obtain an asymptotic description in physical coordinates of the solution, which shows that modified scattering holds. The proof of this global in time existence result relies on the simultaneous bootstrap of some HΓΆlder and Sobolev a priori estimates for the action of iterated Klainerman vector fields on the solutions of the water waves equation. The present volume contains the proof of the Sobolev part of that bootstrap.
β¦ Subjects
Mathematics;Applied;Geometry & Topology;History;Infinity;Mathematical Analysis;Matrices;Number Systems;Popular & Elementary;Pure Mathematics;Reference;Research;Study & Teaching;Transformations;Trigonometry;Science & Math;Mathematics;Algebra & Trigonometry;Calculus;Geometry;Statistics;Science & Mathematics;New, Used & Rental Textbooks;Specialty Boutique
π SIMILAR VOLUMES
Gravity's Shadow: The Search for Gravita
β Harry Collins
π Library
π
2010
π University of Chicago Press
π English
<div>According to the theory of relativity, we are constantly bathed in gravitational radiation. When stars explode or collide, a portion of their mass becomes energy that disturbs the very fabric of the space-time continuum like ripples in a pond. But proving the existence of these waves has been d
Gravity's shadow: the search for gravita
β Harry Collins
π Library
π
2004
π University Of Chicago Press
π English
Gravity's Shadow: The Search for Gravita
β Harry Collins
π Library
π
2004
π University of Chicago Press
π English
<DIV>According to the theory of relativity, we are constantly bathed in gravitational radiation. When stars explode or collide, a portion of their mass becomes energy that disturbs the very fabric of the space-time continuum like ripples in a pond. But proving the existence of these waves has been d
Gravity's shadow : the search for gravit
β Collins, Harry M
π Library
π
2004
π University of Chicago Press
π English
<div>According to the theory of relativity, we are constantly bathed in gravitational radiation. When stars explode or collide, a portion of their mass becomes energy that disturbs the very fabric of the space-time continuum like ripples in a pond. But proving the existence of these waves has been d
Small divisor problem in the theory of t
β Gerard Iooss, Pavel I. Plotnikov
π Library
π
2009
π Amer Mathematical Society
π English
The authors consider doubly-periodic travelling waves at the surface of an infinitely deep perfect fluid, only subjected to gravity g and resulting from the nonlinear interaction of two simply periodic traveling waves making an angle 2[theta] between them. Denoting by [mu] = gL/c2 the dimensionless