半平面上Euler-α方程组的边界层方程整体适定性  

Global well-posedness of the boundary layer equations from Euler-αequations in half plane

作　　者：孙小梅 臧爱彬[2] Sun Xiaomei;Zang Aibin(School of Mathematics,Northwest University,Xi′an 710127,China;School of Mathematics and Computer Science and Center of Applied Mathemacs,Yichun University,Yichun 336000,China)

机构地区：[1]西北大学数学学院,陕西西安710127 [2]宜春学院数学与计算机科学学院和宜春学院应用数学研究中心,江西宜春336000

出　　处：《纯粹数学与应用数学》2021年第1期25-37,共13页Pure and Applied Mathematics

基　　金：国家自然科学基金(11771382).

摘　　要：首先利用形式展开式得到半平面上Euler-α方程组具无滑动边界条件的边界层方程称之为Prandtl型方程.接着构造合适的解析空间,利用抽象Cauchy-Kovalevskaya定理验证该Prandtl型方程局部解的存在唯一性.最后通过求解Prandtl型方程的整体形式解,进而验证得到Prandtl型方程存在整体唯一解.In this paper,we start from the asymptotic expansions of Euler-αequations and derive Prandtl type equations.We also obtain the local existence and uniqueness of the solutions to Prandtl type equations by abstract Cauchy-Kovalevskaya theorem.Furthermore,we discuss on the formal solutions of the vorticity equation of Prandtl equations,then one can verify this solutions is an exact and global-in-time solution of Prandtl type solutions.

关 键 词：Euler-α方程组 Prandtl型方程 抽象Cauchy-Kovalevskaya定理 

分 类 号：O175.29[理学—数学]