Prandtl方程适定性的仿线性化方法

Paralinearization method about the well-posedness of the Prandtl equation

本文主要利用仿线性化的方法研究Prandtl方程对单调初值在Sobolev空间中的局部适定性和解的长时间存在性.相比Nash-Moser迭代方法,该方法的主要优点是对初值的相容性条件和正则性条件要求更低,且证明也更为简洁.

In this paper,by using the paralinearization method,we study the local well-posedness and its lifespan of the Prandtl equation for monotonic data in Sobolev space.Compared with the Nash-Moser iteration method,the main advantages include that the compatibility conditions are removed and the regularity of the initial data is weaker,and the proof is much more concise.