TY - JOUR
T1 - On a Type I Singularity Condition in Terms of the Pressure for the Euler Equations in ℝ3
AU - Chae, Dongho
AU - Constantin, Peter
N1 - Publisher Copyright:
© 2021 The Author(s).
PY - 2022/6/1
Y1 - 2022/6/1
N2 - We prove a blow up criterion in terms of the Hessian of the pressure of smooth solutions u∈ C([0, T); W2,q ℝ3)), q > 3 of the incompressible Euler equations. We show that a blow up at t = T happens only if 'Equation Presented' As consequences of this criterion we show that there is no blow up at t=T if ||D2 p(t)||L∞ ≤ c/(T-t)2 with c < 1 as t ↗ T. Under the additional assumption of ∫0T||u(t)||L∞ (B(x0, ρ)) dt < +∞, we obtain localized versions of these results.
AB - We prove a blow up criterion in terms of the Hessian of the pressure of smooth solutions u∈ C([0, T); W2,q ℝ3)), q > 3 of the incompressible Euler equations. We show that a blow up at t = T happens only if 'Equation Presented' As consequences of this criterion we show that there is no blow up at t=T if ||D2 p(t)||L∞ ≤ c/(T-t)2 with c < 1 as t ↗ T. Under the additional assumption of ∫0T||u(t)||L∞ (B(x0, ρ)) dt < +∞, we obtain localized versions of these results.
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U2 - 10.1093/imrn/rnab014
DO - 10.1093/imrn/rnab014
M3 - Article
AN - SCOPUS:85132948623
SN - 1073-7928
VL - 2022
SP - 9013
EP - 9023
JO - International Mathematics Research Notices
JF - International Mathematics Research Notices
IS - 12
ER -