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arXiv · 1903.07017

Blowup of solutions to the thermal boundary layer problem in two-dimensional incompressible heat conducting flow

Ya-Guang Wang·Shi-Yong Zhu
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Abstract

In this paper, we study the formation of finite time singularities for the solution of the boundary layer equations in the two-dimensional incompressible heat conducting flow. We obtain that the first spacial derivative of the solution blows up in a finite time for the thermal boundary layer problem, for a kind of data which are analytic in the tangential variable but do not satisfy the Oleinik monotonicity condition, by constructing a Lyapunov functional. Moreover, it is observed that the buoyancy coming from the temperature difference in the flow may destabilize the thermal boundary layer.

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Ya-Guang Wang, Shi-Yong Zhu. 2019-03-17. Blowup of solutions to the thermal boundary layer problem in two-dimensional incompressible heat conducting flow. https://arxiv.org/abs/1903.07017

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