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

Tarek M. Elgindi; Nader Masmoudi

doi:10.1007/s00205-019-01457-7

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

Research output: Contribution to journal › Article › peer-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 C^k∩ 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 language	English (US)
Pages (from-to)	1979-2025
Number of pages	47
Journal	Archive for Rational Mechanics and Analysis
Volume	235
Issue number	3
DOIs	https://doi.org/10.1007/s00205-019-01457-7
State	Published - Mar 1 2020

ASJC Scopus subject areas

Analysis
Mathematics (miscellaneous)
Mechanical Engineering

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