Publications related to On global regularity for systems of nonlinear wave equations with the null-condition

Global Regularity For The Nonlinear Wave Equation With Slightly Supercritical Power

Maria Colombo, Silja Noëmi Aline Haffter

We consider the defocusing nonlinear wave equation ❑u D jujp ⠀1u in R3 ⠂ & UOELIG;0; 1/. We prove that for any initial datum with a scaling-subcritical norm bounded by M0 the equation is globally well-posed for p D 5 C i, where i 2 .0; ...

MATHEMATICAL SCIENCE PUBL2023

Mean flow modeling in high-order nonlinear Schrodinger equations

Debbie Eeltink

The evaluation and consideration of the mean flow in wave evolution equations are necessary for the accurate prediction of fluid particle trajectories under wave groups, with relevant implications in several domains, from the transport of pollutants in the ...

2023

A weakly nonlinear amplitude equation approach to the bypass transition in the two-dimensional Lamb–Oseen vortex

François Gallaire, Yves-Marie François Ducimetière

We analytically derive an amplitude equation for the weakly nonlinear evolution of the linearly most amplified response of a non-normal dynamical system. The development generalizes the method proposed in Ducimetière et al. (J. Fluid Mech., vol. 947, 2022, ...

Cambridge University Press2023

Koopman Analysis of Isolated Fronts and Solitons

Jeremy Peter Parker

A Koopman decomposition of a complex system leads to a representation in which nonlinear dynamics appear to be linear. The existence of a linear framework with which to analyze nonlinear dynamical systems brings new strategies for prediction and control, w ...

2020

On Classical Global Solutions of Nonlinear Wave Equations with Large Data

Shuang Miao

This article studies the Cauchy problem for systems of semi-linear wave equations on R3+1 with nonlinear terms satisfying the null conditions. We construct future global-in-time classical solutions with arbitrarily large initial energy. The choice of the l ...

OXFORD UNIV PRESS2019

Wave propagation in periodic buckled beams. Part I: Analytical models and numerical simulations

Alessandro Spadoni, Florian Paul Robert Maurin

Periodic buckled beams possess a geometrically nonlinear, load-deformation relationship and intrinsic length scales such that stable, nonlinear waves are possible. Modeling buckled beams as a chain of masses and nonlinear springs which account for transver ...

Elsevier Science Bv2016

Wave propagation in periodic buckled beams

Florian Paul Robert Maurin

Folding of the earth's crust, wrinkling of the skin, rippling of fruits, vegetables and leaves are all examples of natural structures that can have periodic buckling. Periodic buckling is also present in engineering structures such as compressed lattices, ...

EPFL2015

Low-frequency wave propagation in post-buckled structures

Alessandro Spadoni, Florian Paul Robert Maurin

Nonlinear wave propagation in solids and material structures provides a physical basis to derive nonlinear canonical equations which govern disparate phenomena such as vortex filaments, plasma waves, and traveling loops. Nonlinear waves in solids however r ...

Elsevier2014

Capillary effect on watertable fluctuations in unconfined aquifers

David Andrew Barry

Parlange and Brutsaert [1987] derived a modified Boussinesq equation to account for the capillary effect on watertable dynamics in unconfined aquifers. Barry et al. [1996] solved this equation subject to a periodic boundary condition. Their solution shows ...

American Geophysical Union2013

Method and apparatus for retrieval of amplitude and phase of nonlinear electromagnetic waves

Christian Depeursinge, Etienne Shaffer

The present invention discloses a method and its associated apparatus to retrieve the amplitude and, especially, the phase of nonlinear electromagnetic waves. The application field of the present invention is optical imaging. A sample is probed by coherent ...

2010