Skip to main content
Journal cover image

Boundary layer models of the Hou-Luo scenario

Publication ,  Journal Article
He, S; Kiselev, A
Published in: Journal of Differential Equations
October 15, 2021

Finite time blow up vs global regularity question for 3D Euler equation of fluid mechanics is a major open problem. Several years ago, Luo and Hou [16] proposed a new finite time blow up scenario based on extensive numerical simulations. The scenario is axi-symmetric and features fast growth of vorticity near a ring of hyperbolic points of the flow located at the boundary of a cylinder containing the fluid. An important role is played by a small boundary layer where intense growth is observed. Several simplified models of the scenario have been considered, all leading to finite time blow up [3,2,9,13,11,15]. In this paper, we propose two models that are designed specifically to gain insight in the evolution of fluid near the hyperbolic stagnation point of the flow located at the boundary. One model focuses on analysis of the depletion of nonlinearity effect present in the problem. Solutions to this model are shown to be globally regular. The second model can be seen as an attempt to capture the velocity field near the boundary to the next order of accuracy compared with the one-dimensional models such as [3,2]. Solutions to this model blow up in finite time.

Duke Scholars

Published In

Journal of Differential Equations

DOI

EISSN

1090-2732

ISSN

0022-0396

Publication Date

October 15, 2021

Volume

298

Start / End Page

182 / 204

Related Subject Headings

  • General Mathematics
  • 4904 Pure mathematics
  • 4901 Applied mathematics
  • 0102 Applied Mathematics
  • 0101 Pure Mathematics
 

Citation

APA
Chicago
ICMJE
MLA
NLM
He, S., & Kiselev, A. (2021). Boundary layer models of the Hou-Luo scenario. Journal of Differential Equations, 298, 182–204. https://doi.org/10.1016/j.jde.2021.07.007
He, S., and A. Kiselev. “Boundary layer models of the Hou-Luo scenario.” Journal of Differential Equations 298 (October 15, 2021): 182–204. https://doi.org/10.1016/j.jde.2021.07.007.
He S, Kiselev A. Boundary layer models of the Hou-Luo scenario. Journal of Differential Equations. 2021 Oct 15;298:182–204.
He, S., and A. Kiselev. “Boundary layer models of the Hou-Luo scenario.” Journal of Differential Equations, vol. 298, Oct. 2021, pp. 182–204. Scopus, doi:10.1016/j.jde.2021.07.007.
He S, Kiselev A. Boundary layer models of the Hou-Luo scenario. Journal of Differential Equations. 2021 Oct 15;298:182–204.
Journal cover image

Published In

Journal of Differential Equations

DOI

EISSN

1090-2732

ISSN

0022-0396

Publication Date

October 15, 2021

Volume

298

Start / End Page

182 / 204

Related Subject Headings

  • General Mathematics
  • 4904 Pure mathematics
  • 4901 Applied mathematics
  • 0102 Applied Mathematics
  • 0101 Pure Mathematics