Remarks on Type I Blow-Up for the 3D Euler Equations and the 2D Boussinesq Equations

In this paper, we derive kinematic relations for quantities involving the rate of strain tensor and the Hessian of the pressure for solutions of the 3D Euler equations and the 2D Boussinesq equations. Using these kinematic relations, we prove new blow-up criteria and obtain conditions for the absenc...

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Bibliographic Details
Published inJournal of nonlinear science Vol. 31; no. 5
Main Authors Chae, Dongho, Constantin, Peter
Format Journal Article
LanguageEnglish
Published New York Springer US 01.10.2021
Springer Nature B.V
Subjects
Analysis
Boussinesq equations
Classical Mechanics
Criteria
Economic Theory/Quantitative Economics/Mathematical Methods
Euler-Lagrange equation
Eulers equations
Kinematics
Mathematical analysis
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Tensors
Theoretical
Blow-up criterion
Boussinesq equations
76B03
Type I singularity
Kinematic relations
35Q31
Euler equations
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Summary:In this paper, we derive kinematic relations for quantities involving the rate of strain tensor and the Hessian of the pressure for solutions of the 3D Euler equations and the 2D Boussinesq equations. Using these kinematic relations, we prove new blow-up criteria and obtain conditions for the absence of type I singularity for these equations. We obtain both global and localized versions of the results. Some of the new blow-up criteria and type I conditions improve previous results of Chae and Constantin (Int Math Res Notices rnab014, 2021).
ISSN:0938-8974
1432-1467
DOI:10.1007/s00332-021-09734-0