Prandtl方程的整体适定性和有限时间爆破

Global well-posedness and finite time blowup of the Prandtl equation

本文在解析框架下研究了两类Prandtl型方程的长时间适定性和爆破.对于经典Prandtl方程,本文证明了Paicu和Zhang (2011)得到的解的存在时间长度是最优的.对于从磁流体边界层模型导出的阻尼Prandtl方程,本文证明了小解析初值的整体适定性和对一类大解析初值的有限时间爆破.

In this paper, we study two types of Prandtl equations in the analytical setting. For the classical Prandtl equation, we prove the sharpness for the lifespan of the solution obtained by Paicu and Zhang（2011）.For the Prandtl equation with damping derived from MHD boundary layer, we prove the global well-posedness for small analytic data and finite time blowup for large analytic data.