L Ill-Posedness for a Class of Equations Arising in Hydrodynamics

Tarek M. Elgindi, Nader Masmoudi

Research output: Contribution to journalArticlepeer-review

Abstract

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 n-dimensional Euler equations in the class C1∩ L2(Ω) and also in Ck∩ L2(Ω) where Ω can be the whole space, a smooth bounded domain, or the torus. We also apply our method to the Oldroyd B, surface quasi-geostrophic, and Boussinesq systems.

Original languageEnglish (US)
Pages (from-to)1979-2025
Number of pages47
JournalArchive for Rational Mechanics and Analysis
Volume235
Issue number3
DOIs
StatePublished - Mar 1 2020

ASJC Scopus subject areas

  • Analysis
  • Mathematics (miscellaneous)
  • Mechanical Engineering

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