Strong illposedness of the incompressible Euler equation in integer Cm spaces

By Jean Bourgain, Dong Li. Geometric and Functional Analysis, 2014

117 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Mechanics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/20e65dfef931a2c0dc6c29aae87f9aea66f916eb

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In Applied Mathematics

In Computational Mechanics

In Mathematical Physics

Citations in the corpus

On Kato–Ponce and fractional Leibniz (2016, background): “Further counterexamples In this section we collect further counterexamples for the operator J on divergence-free velocity fields which are deeply connected with the investigation of norm estimates of incompressible Euler equations in Sobolev spaces (see [2, 3, 17] and the references therein).”
Ill-posedness for the Incompressible Euler Equations in Critical Sobolev Spaces (2016, unknown): “During the time interval [0, t∗], particles starting from the arc {(r, θ) : r = N−1, π/4 ≤ θ ≤ π/3} remain in the region {r N−5/6} under the flow Φ(t, ·).”
L∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^\infty $$\end{document} Ill-Posedness for a Class of Equations Ari (2019, methodology): “Another important point is that while the results in [7] are exclusively focused on the Euler equations, our outlook is slightly more general and the application to the Euler equations is just one part of this work.”
Global solutions of 3D incompressible MHD system with mixed partial dissipation and magnetic diffusion near an equilibrium (2019, methodology): “The 3D Navier-Stokes equations with full dissipation have small data global well-posedness while the 3D incompressible Euler equations are ill-posed and have norm inflation in any Sobolev space H or C for any positive integer k [4,5,18].”
Nonuniqueness of Weak Solutions to the SQG Equation (2016, background): “[5,6,47,54]), ̨U is also conjectured to be equal to 1 (only ̨U 1 is known), ̨O D 1=3 (cf.”