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

2019/03/17 by Yaguang Wang, Wang, Ya-Guang, Shi‐Yong Zhu +1
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1903.07017

openalex publication_date 2019/03/17 · openalex created_date 2019/03/22 · openalex updated_date 2026/07/28

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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