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Title: A computational investigation of the finite-time blow-up of the 3D incompressible Euler equations based on the Voigt regularization

We report the results of a computational investigation of two blow-up criteria for the 3D incompressible Euler equations. One criterion was proven in a previous work, and a related criterion is proved here. These criteria are based on an inviscid regularization of the Euler equations known as the 3D Euler-Voigt equations, which are known to be globally well-posed. Moreover, simulations of the 3D Euler-Voigt equations also require less resolution than simulations of the 3D Euler equations for xed values of the regularization parameter α > 0. Therefore, the new blow-up criteria allow one to gain information about possible singularity formation in the 3D Euler equations indirectly; namely, by simulating the better-behaved 3D Euler-Voigt equations. The new criteria are only known to be suficient for blow-up. Therefore, to test the robustness of the inviscid-regularization approach, we also investigate analogous criteria for blow-up of the 1D Burgers equation, where blow-up is well-known to occur.
Authors:
ORCiD logo [1] ;  [2] ;  [3] ;  [4]
  1. Univ. of Nebraska, Lincoln, NE (United States)
  2. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
  3. Texas A & M Univ., College Station, TX (United States); Weizmann Inst. of Science, Rehovot (Israel)
  4. Univ. of Exeter (United Kingdom)
Publication Date:
Report Number(s):
LA-UR-17-23192
Journal ID: ISSN 0935-4964
Grant/Contract Number:
AC52-06NA25396
Type:
Accepted Manuscript
Journal Name:
Theoretical and Computational Fluid Dynamics
Additional Journal Information:
Journal Volume: 32; Journal Issue: 1; Journal ID: ISSN 0935-4964
Publisher:
Springer
Research Org:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org:
USDOE Office of Science (SC). Advanced Scientific Computing Research (ASCR) (SC-21)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; Mathematics; Euler-Voigt; Navier-Stokes-Voigt; Inviscid Regularization, Turbulence Models; Inviscid Regularization; Turbulence Models
OSTI Identifier:
1357141

Larios, Adam, Petersen, Mark R., Titi, Edriss S., and Wingate, Beth. A computational investigation of the finite-time blow-up of the 3D incompressible Euler equations based on the Voigt regularization. United States: N. p., Web. doi:10.1007/s00162-017-0434-0.
Larios, Adam, Petersen, Mark R., Titi, Edriss S., & Wingate, Beth. A computational investigation of the finite-time blow-up of the 3D incompressible Euler equations based on the Voigt regularization. United States. doi:10.1007/s00162-017-0434-0.
Larios, Adam, Petersen, Mark R., Titi, Edriss S., and Wingate, Beth. 2017. "A computational investigation of the finite-time blow-up of the 3D incompressible Euler equations based on the Voigt regularization". United States. doi:10.1007/s00162-017-0434-0. https://www.osti.gov/servlets/purl/1357141.
@article{osti_1357141,
title = {A computational investigation of the finite-time blow-up of the 3D incompressible Euler equations based on the Voigt regularization},
author = {Larios, Adam and Petersen, Mark R. and Titi, Edriss S. and Wingate, Beth},
abstractNote = {We report the results of a computational investigation of two blow-up criteria for the 3D incompressible Euler equations. One criterion was proven in a previous work, and a related criterion is proved here. These criteria are based on an inviscid regularization of the Euler equations known as the 3D Euler-Voigt equations, which are known to be globally well-posed. Moreover, simulations of the 3D Euler-Voigt equations also require less resolution than simulations of the 3D Euler equations for xed values of the regularization parameter α > 0. Therefore, the new blow-up criteria allow one to gain information about possible singularity formation in the 3D Euler equations indirectly; namely, by simulating the better-behaved 3D Euler-Voigt equations. The new criteria are only known to be suficient for blow-up. Therefore, to test the robustness of the inviscid-regularization approach, we also investigate analogous criteria for blow-up of the 1D Burgers equation, where blow-up is well-known to occur.},
doi = {10.1007/s00162-017-0434-0},
journal = {Theoretical and Computational Fluid Dynamics},
number = 1,
volume = 32,
place = {United States},
year = {2017},
month = {4}
}