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arXiv:1405.2478 [math.AP]AbstractReferencesReviewsResources

Ill-posedness results in critical spaces for some equations arising in hydrodynamics

Tarek M. Elgindi, Nader Masmoudi

Published 2014-05-10, updated 2017-07-15Version 3

Many questions related to well-posedness/ill-posedness in critical spaces for hydrodynamic equations have been open for many years. Some of them have only recently been settled. In this article we give a new approach to studying norm inflation (in some critical spaces) for a wide class of equations arising in hydrodynamics. As an application, we prove strong ill-posedness of the $d$-dimensional Euler equations in the class $C^1\cap L^2.$ We give two proofs of this result in sections 8 and 9.

Comments: Fixed some typos. Fixed an error in the proof of Proposition 3.1. Added a short section on the Euler equations in $C^k$
Categories: math.AP
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