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arXiv · 1807.10341

On stability of blow-up solutions of the Burgers vortex type for the Navier-Stokes equations with a linear strain

Yasunori Maekawa·Hideyuki Miura·Christophe Prange
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Abstract

We study the three-dimensional Navier-Stokes equations in the presence of the axisymmetric linear strain, where the strain rate depends on time in a specific manner. It is known that the system admits solutions which blow up in finite time and whose profiles are in a backward self-similar form of the familiar Burgers vortices. In this paper it is shown that the existing stability theory of the Burgers vortex leads to the stability of these blow-up solutions as well. The secondary blow-up is also observed when the strain rate is relatively weak.

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Yasunori Maekawa, Hideyuki Miura, Christophe Prange. 2018-07-26. On stability of blow-up solutions of the Burgers vortex type for the Navier-Stokes equations with a linear strain. https://doi.org/10.1007/s00021-019-0450-5

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