Non-Uniform Dependence on Initial Data of Solutions to the Euler Equations of Hydrodynamics

We show that continuous dependence on initial data of solutions to the Euler equations of incompressible hydrodynamics is optimal. More precisely, we prove that the data-to-solution map is not uniformly continuous in Sobolev H s (Ω) topology for any if the domain Ω is the (flat) torus and for any s...

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Bibliographic Details
Published in:	Communications in mathematical physics Vol. 296; no. 1; pp. 285 - 301
Main Authors:	Himonas, A. Alexandrou, Misiołek, Gerard
Format:	Journal Article
Language:	English
Published:	Berlin/Heidelberg Springer-Verlag 01-05-2010
Subjects:	Classical and Quantum Gravitation Complex Systems Mathematical and Computational Physics Mathematical Physics Physics Physics and Astronomy Quantum Physics Relativity Theory Theoretical Cauchy Problem High Frequency Part Diffeomorphism Group Euler Equation Continuous Dependence
Online Access:	Get full text
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Summary:	We show that continuous dependence on initial data of solutions to the Euler equations of incompressible hydrodynamics is optimal. More precisely, we prove that the data-to-solution map is not uniformly continuous in Sobolev H s (Ω) topology for any if the domain Ω is the (flat) torus and for any s > 0 if the domain is the whole space .
ISSN:	0010-3616 1432-0916
DOI:	10.1007/s00220-010-0991-1