Quasi-Periodic Traveling Waves on an Infinitely Deep Perfect Fluid Under Gravity

Quasi-Periodic Traveling Waves on an Infinitely Deep Perfect Fluid Under Gravity PDF Author: Roberto Feola
Publisher: Ams American Mathematical Society
ISBN: 9781470477714
Category : Science
Languages : en
Pages : 0

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Book Description
We consider the gravity water waves system with a periodic one-dimensional interface in infinite depth and we establish the existence and the linear stability of small amplitude, quasi-periodic in time, traveling waves. This provides the first existence result of quasi-periodic water waves solutions bifurcating from a completely resonant elliptic fixed point. The proof is based on a Nash-Moser scheme, Birkhoff normal form methods and pseudo differential calculus techniques. We deal with the combined problems of small divisors and the fully-nonlinear nature of the equations. The lack of parameters, like the capillarity or the depth of the ocean, demands a refined nonlinear bifurcation analysis involving several nontrivial resonant wave interactions, as the well-known “Benjamin-Feir resonances”. We develop a novel normal form approach to deal with that. Moreover, by making full use of the Hamiltonian structure, we are able to provide the existence of a wide class of solutions which are free from restrictions of parity in the time and space variables.

Quasi-Periodic Traveling Waves on an Infinitely Deep Perfect Fluid Under Gravity

Quasi-Periodic Traveling Waves on an Infinitely Deep Perfect Fluid Under Gravity PDF Author: Roberto Feola
Publisher: Ams American Mathematical Society
ISBN: 9781470477714
Category : Science
Languages : en
Pages : 0

Get Book Here

Book Description
We consider the gravity water waves system with a periodic one-dimensional interface in infinite depth and we establish the existence and the linear stability of small amplitude, quasi-periodic in time, traveling waves. This provides the first existence result of quasi-periodic water waves solutions bifurcating from a completely resonant elliptic fixed point. The proof is based on a Nash-Moser scheme, Birkhoff normal form methods and pseudo differential calculus techniques. We deal with the combined problems of small divisors and the fully-nonlinear nature of the equations. The lack of parameters, like the capillarity or the depth of the ocean, demands a refined nonlinear bifurcation analysis involving several nontrivial resonant wave interactions, as the well-known “Benjamin-Feir resonances”. We develop a novel normal form approach to deal with that. Moreover, by making full use of the Hamiltonian structure, we are able to provide the existence of a wide class of solutions which are free from restrictions of parity in the time and space variables.

Quasi-Periodic Traveling Waves on an Infinitely Deep Perfect Fluid Under Gravity

Quasi-Periodic Traveling Waves on an Infinitely Deep Perfect Fluid Under Gravity PDF Author: Roberto Feola
Publisher: American Mathematical Society
ISBN: 1470468778
Category : Mathematics
Languages : en
Pages : 170

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Simple Supercuspidal $L$-Packets of Quasi-Split Classical Groups

Simple Supercuspidal $L$-Packets of Quasi-Split Classical Groups PDF Author: Masao Oi
Publisher: American Mathematical Society
ISBN: 1470469561
Category : Mathematics
Languages : en
Pages : 174

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Asymptotic Completeness for a Scalar Quasilinear Wave Equation Satisfying the Weak Null Condition

Asymptotic Completeness for a Scalar Quasilinear Wave Equation Satisfying the Weak Null Condition PDF Author: Dongxiao Yu
Publisher: American Mathematical Society
ISBN: 1470470489
Category : Mathematics
Languages : en
Pages : 140

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Cubical Models of $(infty ,1)$-Categories

Cubical Models of $(infty ,1)$-Categories PDF Author: Brandon Doherty
Publisher: American Mathematical Society
ISBN: 1470468948
Category : Mathematics
Languages : en
Pages : 122

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On Refined Conjectures of Birch and Swinnerton-Dyer Type for Hasse–Weil–Artin $L$-Series

On Refined Conjectures of Birch and Swinnerton-Dyer Type for Hasse–Weil–Artin $L$-Series PDF Author: David Burns
Publisher: American Mathematical Society
ISBN: 1470469669
Category : Mathematics
Languages : en
Pages : 168

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A Plethora of Cluster Structures on $GL_n$

A Plethora of Cluster Structures on $GL_n$ PDF Author: M. Gekhtman
Publisher: American Mathematical Society
ISBN: 1470469707
Category : Mathematics
Languages : en
Pages : 116

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Stratified Noncommutative Geometry

Stratified Noncommutative Geometry PDF Author: David Ayala
Publisher: American Mathematical Society
ISBN: 1470469626
Category : Mathematics
Languages : en
Pages : 272

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Extreme Superposition: High-Order Fundamental Rogue Waves in the Far-Field Regime

Extreme Superposition: High-Order Fundamental Rogue Waves in the Far-Field Regime PDF Author: Deniz Bilman
Publisher: American Mathematical Society
ISBN: 1470471213
Category : Mathematics
Languages : en
Pages : 102

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A Comparison Theorem for Semi-Abelian Schemes over a Smooth Curve

A Comparison Theorem for Semi-Abelian Schemes over a Smooth Curve PDF Author: Fabien Trihan
Publisher: American Mathematical Society
ISBN: 1470469693
Category : Mathematics
Languages : en
Pages : 228

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