GLOBAL WELL-POSEDNESS AND REGULARITY OF WEAK SOLUTIONS TO THE PRANDTL'S SYSTEM

We continue our study on the global solution to the two-dimensional Prandtl's system for unsteady boundary layers in the class considered by Oleinik, provided that the pressure is favorable. First, by using a different method from [Z. Xin and L. Zhang, Adv. Math., 181 (2004), pp. 88--133], we gave a direct proof of existence of a global weak solution by a direct BV estimate. Then we prove the uniqueness and continuous dependence on data of such a weak solution to the initial boundary value problem. Finally, we show the smoothness of the weak solutions and then the global existence of smooth solutions.