The van Dommelen and Shen singularity in the Prandtl equations

Igor Kukavica; Vlad Vicol; Fei Wang

doi:10.1016/j.aim.2016.11.013

The van Dommelen and Shen singularity in the Prandtl equations

Igor Kukavica, Vlad Vicol, Fei Wang

Mathematics

Research output: Contribution to journal › Article › peer-review

44 Scopus citations

Abstract

In 1980, van Dommelen and Shen provided a numerical simulation that predicted the spontaneous generation of a singularity in the Prandtl boundary layer equations from a smooth initial datum, for a nontrivial Euler background. In this paper we prove this numerical conjecture by rigorously establishing the finite time blowup of the boundary layer thickness.

Original language	English (US)
Pages (from-to)	288-311
Number of pages	24
Journal	Advances in Mathematics
Volume	307
DOIs	https://doi.org/10.1016/j.aim.2016.11.013
State	Published - Feb 5 2017

All Science Journal Classification (ASJC) codes

General Mathematics

Keywords

Boundary layer separation
Prandtl equations

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10.1016/j.aim.2016.11.013

Cite this

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title = "The van Dommelen and Shen singularity in the Prandtl equations",

abstract = "In 1980, van Dommelen and Shen provided a numerical simulation that predicted the spontaneous generation of a singularity in the Prandtl boundary layer equations from a smooth initial datum, for a nontrivial Euler background. In this paper we prove this numerical conjecture by rigorously establishing the finite time blowup of the boundary layer thickness.",

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T1 - The van Dommelen and Shen singularity in the Prandtl equations

AU - Kukavica, Igor

AU - Vicol, Vlad

AU - Wang, Fei

PY - 2017/2/5

Y1 - 2017/2/5

N2 - In 1980, van Dommelen and Shen provided a numerical simulation that predicted the spontaneous generation of a singularity in the Prandtl boundary layer equations from a smooth initial datum, for a nontrivial Euler background. In this paper we prove this numerical conjecture by rigorously establishing the finite time blowup of the boundary layer thickness.

AB - In 1980, van Dommelen and Shen provided a numerical simulation that predicted the spontaneous generation of a singularity in the Prandtl boundary layer equations from a smooth initial datum, for a nontrivial Euler background. In this paper we prove this numerical conjecture by rigorously establishing the finite time blowup of the boundary layer thickness.

KW - Boundary layer separation

KW - Prandtl equations

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EP - 311

JO - Advances in Mathematics

JF - Advances in Mathematics

ER -

The van Dommelen and Shen singularity in the Prandtl equations

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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