BLOWUP OF SOLUTIONS TO THE THERMAL BOUNDARY LAYER PROBLEM IN TWO-DIMENSIONAL INCOMPRESSIBLE HEAT CONDUCTING FLOW

被引：2

作者：

Wang, Yaguang ^{[1
,2
]}

Zhu, Shiyong ^{[3
]}

机构：

[1] Shanghai Jiao Tong Univ, Sch Math Sci, MOE LSC, Shanghai 200240, Peoples R China

[2] Shanghai Jiao Tong Univ, SHL MAC, Shanghai 200240, Peoples R China

[3] Shanghai Jiao Tong Univ, Sch Math Sci, Shanghai 200240, Peoples R China

来源：

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | 2020年 / 19卷 / 06期

基金：

中国国家自然科学基金;

关键词：

Thermal boundary layer problem; non-monotonic datum; blowup of analytic solution; singularity; Lyapunov functional; NAVIER-STOKES EQUATION; ZERO VISCOSITY LIMIT; WELL-POSEDNESS; ANALYTIC SOLUTIONS; PRANDTL EQUATIONS; ILL-POSEDNESS; HALF-SPACE; EXISTENCE; SYSTEM;

D O I：

10.3934/cpaa.2020141

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：3233 / 3244

页数：12

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