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.
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 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.
Publisher Copyright:
© 2019, Springer-Verlag GmbH Germany, part of Springer Nature.
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 -