关于Prandtl方程组整体弱解的存在性

On the Global Existence of Weak Solutions to the Prandtl's System

考虑非定常Prandtl方程组整体弱解的存在性.引进Crocco变换,将Prandtl方程组(1)、(2)转化成一个初边值问题(3).通过对问题(3)的正则化问题作一致估计,类似文Xin Zhang或Zhang Zhao的方法可证明整体弱解的存在性.这改进已有的Prandtl方程组存在整体BV弱解的条件.

In this paper, we consider the global existence of weak solutions to the non-stationary Prandtl's system (1)、(2). However,we consider the initial-boundary problem (3) instead of the Prandtl's system via Crocco transformation and obtain some uniform estimates of the solutions to the regularized problem of (3) under some assumptions. Similar to the argument in the paper by Xin-Zhang or the paper by Zhang-Zhao,we can prove the global existence of weak solutions and the conditions for the global existence have been improved.