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Thursday, 08 September 2016 21:27

Finite time blow up in the hyperbolic Boussinesq system

 

Alexander Kiselev, and Changhui Tan

Advances in Mathematics, Volume 325, pp. 34-55 (2018).


Abstract

In recent work of Luo and Hou, a new scenario for finite time blow up in solutions of 3D Euler equation has been proposed. The scenario involves a ring of hyperbolic points of the flow located at the boundary of a cylinder. In this paper, we propose a two dimensional model that we call “hyperbolic Boussinesq system”. This model is designed to provide insight into the hyperbolic point blow up scenario. The model features an incompressible velocity vector field, a simplified Biot–Savart law, and a simplified term modeling buoyancy. We prove that finite time blow up happens for a natural class of initial data.


   doi:10.1016/j.aim.2017.11.019
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Read 7463 times Last modified on Monday, 19 July 2021 00:43