Counter-examples to concentration-cancellation
type: Item
instance of: scholarly article
title: Counter-examples to concentration-cancellation
zbMATH Open document ID: 1160.35003
published in: Archive for Rational Mechanics and Analysis
publication date: 2008-12-01T00:00:00Z
review text: This paper consider the incompressible Euler equations. In general in order to show the existence of weak solutions to Euler equations, an approximate solution sequence was constructed either by smoothing the initial data or by adding to Euler equations a small viscosity. By the property of concentration-cancellation, all the extracted \(L^2_{loc}\) weak limits still satisfy the Euler equations, through the approximate solution sequence does not converge strongly in \(L^2_{loc}\). So up to now, for the two-dimensional case, the weak limits of approximate solutions have always been observed to be solution of the Euler equations. Thus, one want to know if the property of concentration-cancellation does generalize to the space \(L^2\) of the energy estimates. It makes sense also in the less restrictive framework \(L^2_{loc}\). So the authors develop a WKB analysis and give a negative reply to the last question.
reviewed by: Cheng He
Mathematics Subject Classification ID: 35-02
Mathematics Subject Classification ID: 35Q35
Mathematics Subject Classification ID: 76B03
zbMATH DE Number: 5375976
zbMATH Keywords: Euler equations
zbMATH Keywords: concentration-cancellation
zbMATH Keywords: counter-example
author: Christophe Cheverry
author: Olivier Guès
MaRDI profile type: Publication
full work available at URL: s00205-008-0132-6
OpenAlex ID: W2018888168
cites work: Lifespan and blow-up of solutions of the quasilinear wave equations in two dimensions. II
cites work: Q4663720
cites work: Q4210480
cites work: Propagation of oscillations in real vanishing viscosity limit
cites work: Cascade of phases in turbulent flows
cites work: Q5494610
cites work: Q3514581
cites work: Oscillations fortes sur un champ linéairement dégénéré
cites work: Large-amplitude high-frequency waves for quasilinear hyperbolic systems
cites work: Existence de Nappes de Tourbillon en Dimension Deux
cites work: Oscillations and concentrations in weak solutions of the incompressible fluid equations
cites work: Nonlinear instability in an ideal fluid
cites work: Q5286423
cites work: On the nonlinear instability of Euler and Prandtl equations.
cites work: On Pressureless Gases Driven by a Strong Inhomogeneous Magnetic Field
cites work: Generic rigorous asymptotic expansions for weakly nonlinear multidimensional oscillatory waves
cites work: Coherent and focusing multidimensional nonlinear geometric optics
cites work: Q4884692
cites work: Q3152412
cites work: Vorticity and incompressible flow
cites work: Compressible fluid flow and systems of conservation laws in several space variables
cites work: Global smooth solutions of some quasilinear hyperbolic systems with large data
cites work: The weak vorticity formulation of the 2-d euler equations and concentration-cancellation
cites work: Q5337988
DOI: 10.1007/S00205-008-0132-6
description: scientific article; zbMATH DE number 5375976