Abstract
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).
Original language | English (US) |
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Article number | 77 |
Journal | Journal of Nonlinear Science |
Volume | 31 |
Issue number | 5 |
DOIs | |
State | Published - Oct 2021 |
All Science Journal Classification (ASJC) codes
- Modeling and Simulation
- General Engineering
- Applied Mathematics
Keywords
- Blow-up criterion
- Boussinesq equations
- Euler equations
- Kinematic relations
- Type I singularity