二维可压缩Prandtl方程倒流点的存在性

Abstract

Abstract:

In this paper, we study the back-flow problem of the two-dimensional unsteady compressible Prandtl boundary layer equations. By using the maximum principle, we obtain that a first back-flow point should appear on the boundary $\left\{y=0\right\}$ if back-flow occurs under Oleinik's monotonicity assumption. Moreover, when the pressure gradient of the outer flow is adverse and the initial velocity satisfies certain growth condition, we obtain the existence of a back-flow point of the compressible Prandtl boundary layer by Lyapunov functional method. Finally, an example of the existence of the back-flow point is given.

Key words: Compressible Prandtl equation, Back-flow point, The maximum principle, Adverse pressure gradient, Lyapunov functional

CLC Number:

O175.29

Zou Yonghui,Xu Xin. Existence of Back-Flow Point for the Two-Dimensional Compressible Prandtl Equation[J].Acta mathematica scientia,Series A, 2023, 43(3): 691-701.

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References 36

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Existence of Back-Flow Point for the Two-Dimensional Compressible Prandtl Equation

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