2015/12/24 by Adam Larios, Mark Petersen, Larios, Adam +5
Engineering · Mathematics · #35Q30 #76A10 #76B03 #76D03 #76F20 #76F55 #76F65 #76W05 #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Gas Dynamics and Kinetic Theory #Navier-Stokes equation solutions #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.1512.07877
openalex publication_date 2015/12/24 · openalex created_date 2023/02/16 · openalex updated_date 2026/07/28
We report the results of a computational investigation of two blow-up\ncriteria for the 3D incompressible Euler equations. One criterion was proven in\na previous work, and a related criterion is proved here. These criteria are\nbased on an inviscid regularization of the Euler equations known as the 3D\nEuler-Voigt equations, which are known to be globally well-posed. Moreover,\nsimulations of the 3D Euler-Voigt equations also require less resolution than\nsimulations of the 3D Euler equations for fixed values of the regularization\nparameter \α>0. Therefore, the new blow-up criteria allow one to gain\ninformation about possible singularity formation in the 3D Euler equations\nindirectly; namely, by simulating the better-behaved 3D Euler-Voigt equations.\nThe new criteria are only known to be sufficient for blow-up. Therefore, to\ntest the robustness of the inviscid-regularization approach, we also\ninvestigate analogous criteria for blow-up of the 1D Burgers equation, where\nblow-up is well-known to occur.\n