Journal
JOURNAL OF NONLINEAR SCIENCE
Volume 28, Issue 6, Pages 2217-2247Publisher
SPRINGER
DOI: 10.1007/s00332-017-9370-9
Keywords
Self-similar singularity; Axisymmetric incompressible flow; Stabilizing effect of convection; 35Q31
Categories
Funding
- NSF [DMS-1613861, DMS-1318377]
- Hong Kong RGC grant [ECS 26300716]
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [1613861] Funding Source: National Science Foundation
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We study a family of 3D models for the incompressible axisymmetric Euler and Navier-Stokes equations. The models are derived by changing the strength of the convection terms in the equations written using a set of transformed variables. The models share several regularity results with the Euler and Navier-Stokes equations, including an energy identity, the conservation of a modified circulation quantity, the BKM criterion and the Prodi-Serrin criterion. The inviscid models with weak convection are numerically observed to develop stable self-similar singularity with the singular region traveling along the symmetric axis, and such singularity scenario does not seem to persist for strong convection.
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