Stability of Blowup for a 1D Model of Axisymmetric 3D Euler Equation


Journal Article

© 2016, Springer Science+Business Media New York. The question of the global regularity versus finite- time blowup in solutions of the 3D incompressible Euler equation is a major open problem of modern applied analysis. In this paper, we study a class of one-dimensional models of the axisymmetric hyperbolic boundary blow-up scenario for the 3D Euler equation proposed by Hou and Luo (Multiscale Model Simul 12:1722–1776, 2014) based on extensive numerical simulations. These models generalize the 1D Hou–Luo model suggested in Hou and Luo Luo and Hou (2014), for which finite-time blowup has been established in Choi et al. (arXiv preprint. arXiv:1407.4776, 2014). The main new aspects of this work are twofold. First, we establish finite-time blowup for a model that is a closer approximation of the three-dimensional case than the original Hou–Luo model, in the sense that it contains relevant lower-order terms in the Biot–Savart law that have been discarded in Hou and Luo Choi et al. (2014). Secondly, we show that the blow-up mechanism is quite robust, by considering a broader family of models with the same main term as in the Hou–Luo model. Such blow-up stability result may be useful in further work on understanding the 3D hyperbolic blow-up scenario.

Full Text

Duke Authors

Cited Authors

  • Do, T; Kiselev, A; Xu, X

Published Date

  • December 1, 2018

Published In

Volume / Issue

  • 28 / 6

Start / End Page

  • 2127 - 2152

Electronic International Standard Serial Number (EISSN)

  • 1432-1467

International Standard Serial Number (ISSN)

  • 0938-8974

Digital Object Identifier (DOI)

  • 10.1007/s00332-016-9340-7

Citation Source

  • Scopus