TY - JOUR
T1 - L∞ Ill-Posedness for a Class of Equations Arising in Hydrodynamics
AU - Elgindi, Tarek M.
AU - Masmoudi, Nader
N1 - Funding Information:
Both authors were partially supported by NSF Grant DMS-1211806. The first author was also supported by NSF Grant DMS-1402357 and DMS-1817134. The first author thanks Gautam Iyer for motivating him to ?write down? the C 1 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C^1$$\end{document} results. The authors would also like thank the anonymous referees for their comments which greatly improved the paper. The second author was also supported by NSF Grant DMS-1716466.
Funding Information:
Both authors were partially supported by NSF Grant DMS-1211806. The first author was also supported by NSF Grant DMS-1402357 and DMS-1817134. The first author thanks Gautam Iyer for motivating him to “write down” the C 1 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C^1$$\end{document} results. The authors would also like thank the anonymous referees for their comments which greatly improved the paper. The second author was also supported by NSF Grant DMS-1716466.
PY - 2020/3/1
Y1 - 2020/3/1
N2 - 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.
AB - 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.
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U2 - 10.1007/s00205-019-01457-7
DO - 10.1007/s00205-019-01457-7
M3 - Article
AN - SCOPUS:85075339457
VL - 235
SP - 1979
EP - 2025
JO - Archive for Rational Mechanics and Analysis
JF - Archive for Rational Mechanics and Analysis
SN - 0003-9527
IS - 3
ER -