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

Yaguang Wang; Shiyong Zhu

doi:10.3934/cpaa.2020141

Article Contents

2020, Volume 19, Issue 6: 3233-3244. Doi: 10.3934/cpaa.2020141

This issue Previous Article Ricci curvature of conformal deformation on compact 2-manifolds Next Article Some global dynamics of a Lotka-Volterra competition-diffusion-advection system

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

Yaguang Wang^1, and
Shiyong Zhu^2, ,

1.
School of Mathematical Sciences, MOE-LSC and SHL-MAC, , Shanghai Jiao Tong University, Shanghai 200240, China
2.
School of Mathematical Sciences, , Shanghai Jiao Tong University, Shanghai 200240, China

^* Corresponding author
^* Corresponding author

Received: May 31, 2019

Revised: October 31, 2019

Published: March 2020

This research was partially supported by National Natural Science Foundation of China (NNSFC) under Grant No. 11631008

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Abstract

In this paper, we study the formation of singularities in a finite time for the solution of the boundary layer equations in the two-dimensional incompressible heat conducting flow. We obtain that the first order 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 using a Lyapunov functional approach. It is observed that the buoyancy coming from the temperature difference in the flow may destabilize the thermal boundary layer.

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Mathematics Subject Classification: 35Q30, 76D10.

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