Almost Global Existence for the 3D Prandtl Boundary Layer Equations

被引：12
|
作者：
Lin, Xueyun [1 ,2 ]
Zhang, Ting [1 ]
机构：
[1] Zhejiang Univ, Sch Math Sci, Hangzhou 310027, Zhejiang, Peoples R China
[2] Fuzhou Univ, Coll Math & Comp Sci, Fuzhou 350108, Fujian, Peoples R China
来源：
ACTA APPLICANDAE MATHEMATICAE | 2020年 / 169卷 / 01期
基金：
中国国家自然科学基金;
关键词：
Prandtl equations; Almost global existence; Littlewood-Paley theory; NAVIER-STOKES EQUATION; ZERO VISCOSITY LIMIT; TIME WELL-POSEDNESS; ANALYTIC SOLUTIONS; ILL-POSEDNESS; HALF-SPACE; MONOTONICITY; SYSTEM; EULER;
D O I：
10.1007/s10440-019-00303-y
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we prove the almost global existence of classical solutions to the 3D Prandtl system with the initial data which lie within epsilon of a stable shear flow. Using anisotropic Littlewood-Paley energy estimates in tangentially analytic norms and introducing new linearly-good unknowns, we prove that the 3D Prandtl system has a unique solution with the lifespan of which is greater than exp(epsilon(-1)/ log(epsilon(-1))). This result extends the work obtained by Ignatova and Vicol (Arch. Ration. Mech. Anal. 2:809-848, 2016) on the 2D Prandtl equations to the three-dimensional setting.
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页码：383 / 410
页数：28
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