Ill-posedness of the quasilinear wave equation in the space 𝐻7/4(ln𝐻)−𝛽in ℝ2+1

Publications associées (29)

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Efficient algorithms for wave problems

Boris Bonev

Wave phenomena manifest in nature as electromagnetic waves, acoustic waves, and gravitational waves among others. Their descriptions as partial differential equations in electromagnetics, acoustics, and fluid dynamics are ubiquitous in science and engineer ...

EPFL2021

Numerical simulation of sediment dynamics with free surface flows

Arwa Mrad

We present a numerical model for the simulation of 3D mono-dispersed sediment dynamics in a Newtonian flow with free surfaces. The physical model is a macroscopic model for the transport of sediment based on a sediment concentration with a single momentum ...

EPFL2021

Multipolar origin of electromagnetic transverse force resulting from TE/TM wave interference

Olivier Martin, Karim Achouri, Andrei Kiselev

In this paper, we aim at unveiling the underlying physical mechanism for transversal optical forces, appearing due to the simultaneous illumination of a spherical object with two plane waves possessing different polarizations. The appearance of such a tran ...

2021

Finite-time stabilization in optimal time of homogeneous quasilinear hyperbolic systems in one dimensional space

Hoài-Minh Nguyên

We consider the finite-time stabilization of homogeneous quasilinear hyperbolic systems with one side controls and with nonlinear boundary condition at the other side. We present time-independent feedbacks leading to the finite-time stabilization in any ti ...

2020

On long time behavior of solutions to nonlinear dispersive equations

Stefano Francesco Burzio

In part I, we address the issue of existence of solutions for Cauchy problems involving nonlinear hyperbolic equations for initial data in Sobolev spaces with scaling subcritical regularity. In particular, we analyse nonlinear estimates for null-forms in t ...

EPFL2020

Symplectic dynamical low rank approximation of wave equations with random parameters

Fabio Nobile, Eleonora Musharbash, Eva Vidlicková

In this paper we propose a dynamical low-rank strategy for the approximation of second order wave equations with random parameters. The governing equation is rewritten in Hamiltonian form and the approximate solution is expanded over a set of 2S dynamical ...

2020

Nonlinear evolution of the centrifugal instability using a semilinear model

François Gallaire, Eunok Yim

We study the nonlinear evolution of the axisymmetric centrifugal instability developing on a columnar anticyclone with a Gaussian angular velocity using a semilinear approach. The model consists of two coupled equations: one for the linear evolution of the ...

Cambridge University Press2020

Effective Models and Numerical Homogenization for Wave Propagation in Heterogeneous Media on Arbitrary Timescales

Timothée Noé Pouchon, Assyr Abdulle

A family of effective equations for wave propagation in periodic media for arbitrary timescales O(epsilon-alpha), where epsilon MUCH LESS-THAN1 is the period of the tensor describing the medium, is proposed. The well-posedness of the effective equations of ...

SPRINGER2020

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

Time and space adaptivity of the wave equation discretized in time by a second-order scheme

Marco Picasso, Olga Gorynina

The aim of this paper is to obtain a posteriori error bounds of optimal order in time and space for the linear second-order wave equation discretized by the Newmark scheme in time and the finite element method in space. An error estimate is derived in the ...

2019

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