• Corpus ID: 118542955

Finite Time Blow-up of a 3D Model for Incompressible Euler Equations

@article{Hou2012FiniteTB,
  title={Finite Time Blow-up of a 3D Model for Incompressible Euler Equations},
  author={Thomas Y. Hou and Zhen Lei},
  journal={arXiv: Analysis of PDEs},
  year={2012}
}
  • T. Hou, Zhen Lei
  • Published 23 March 2012
  • Mathematics
  • arXiv: Analysis of PDEs
We investigate the role of convection on its large time behavior of 3D incompressible Euler equations. In [15], we constructed a new 3D model by neglecting the convection term from the reformulated axisymmetric Navier-Stokes equations. This model preserves almost all the properties of the full Navier-Stokes equations, including an energy identity for smooth solutions. The numerical evidence presented in [15] seems to support that the 3D model may develop a finite time singularity. In this paper… 
Singularities of solutions to compressible Euler equations with vacuum
Presented are two results on the formation of finite time singularities of solutions to the compressible Euler equations in two and three space dimensions for isentropic, polytropic, ideal fluid

References

SHOWING 1-10 OF 24 REFERENCES
On singularity formation of a 3D model for incompressible Navier–Stokes equations
On the finite‐time singularities of the 3D incompressible Euler equations
We prove the finite‐time vorticity blowup, in the pointwise sense, for solutions of the 3D incompressible Euler equations assuming some conditions on the initial data and its corresponding solutions
Improved Geometric Conditions for Non-Blowup of the 3D Incompressible Euler Equation
This is a follow-up of our recent article Deng et al. (2004). In Deng et al. (2004), we derive some local geometric conditions on vortex filaments which can prevent finite time blowup of the 3D
Numerical computation of 3D incompressible ideal fluids with swirl.
TLDR
This work investigates numerically the question of blowup in finite time for the «swirling flow» of the three-dimensional incompressible Euler equations using rotational symmetry and solves the elliptic equation relating vorticity to velocity with the multigrid method.
Evidence for a Singularity of the Three Dimensional, Incompressible Euler Equations
Three‐dimensional, incompressible Euler calculations of the interaction of perturbed antiparallel vortex tubes using smooth initial profiles in a bounded domain with bounded initial vorticity are
Note on loss of regularity for solutions of the 3—D incompressible euler and related equations
One of the central problems in the mathematical theory of turbulence is that of breakdown of smooth (indefinitely differentiable) solutions to the equations of motion. In 1934 J. Leray advanced the
Blow-up or no blow-up? A unified computational and analytic approach to 3D incompressible Euler and Navier–Stokes equations
  • T. Hou
  • Mathematics
    Acta Numerica
  • 2009
Whether the 3D incompressible Euler and Navier–Stokes equations can develop a finite-time singularity from smooth initial data with finite energy has been one of the most long-standing open
Dynamic Stability of the 3D Axi-symmetric Navier-Stokes Equations with Swirl
In this paper, we study the dynamic stability of the 3D axisymmetric NavierStokes Equations with swirl. To this purpose, we propose a new one-dimensional (1D) model which approximates the
On the Euler equations of incompressible fluids
Euler equations of incompressible fluids use and enrich many branches of mathematics, from integrable systems to geometric analysis. They present important open physical and mathematical problems.
Dynamic Depletion of Vortex Stretching and Non-Blowup of the 3-D Incompressible Euler Equations
TLDR
The numerical results demonstrate that the maximum vorticity does not grow faster than doubly exponential in time, up to t = 19, beyond the singularity time t = 18.7 predicted by Kerr's computations.
...
...