Long wave asymptotics for the Euler-Korteweg system
type: Item
instance of: scholarly article
title: Long wave asymptotics for the Euler-Korteweg system
zbMATH Open document ID: 1391.35323
DOI: 10.4171/RMI/985
author: Sylvie Benzoni-Gavage
author: David Chiron
published in: Revista Matemática Iberoamericana
publication date: 2018-04-05T00:00:00Z
review text: The Euler-Korteweg system EK is a general nonlinear waves model in mathematical physics. In particular, this includes the fluid formulation of the nonlinear Schrödinger equation (NLS). Different asymptotic regimes can be considered, regarding the length and the amplitude of waves. One is the free wave regime, which yields long acoustic waves of small amplitude. The other regimes describe a single wave or two counter propagating waves. It is shown that in one space dimension those waves are governed either by inviscid Burgers or by Korteweg-de Vries equations, depending on the spatiotemporal and amplitude scalings. In higher dimensions, those waves are shown to solve the Kadomtsev-Petviashvili equations. Error bounds are provided in all cases. These results extend earlier work on defocusing NLS equation, and sheds light on the qualitative behavior of solutions to EK, which is a highly nonlinear system of PDEs much less understood than NLS.
reviewed by: Piotr Biler
Mathematics Subject Classification ID: 35Q35
Mathematics Subject Classification ID: 76Q05
Mathematics Subject Classification ID: 35Q53
Mathematics Subject Classification ID: 35Q55
Mathematics Subject Classification ID: 35C07
Mathematics Subject Classification ID: 35B45
zbMATH DE Number: 6856507
zbMATH Keywords: capillary fluids
zbMATH Keywords: Euler-Korteweg system
zbMATH Keywords: Korteweg-de Vries equation
zbMATH Keywords: Kadomtsev-Petviashvili equation
zbMATH Keywords: weakly transverse Boussinesq system
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 6856507