论文标题
Hele-shaw流量的规律性与源和漂移
Regularity of Hele-Shaw Flow with source and drift
论文作者
论文摘要
在本文中，我们研究了Hele-shaw流的规律性特性，其中源和漂移存在于进化中。更具体地说，我们认为Hölder连续来源和Lipschitz连续漂移。我们表明，如果溶液的自由边界在局部靠近Lipschitz图，那么鉴于Lipschitz常数很小，它确实是Lipschitz。当没有漂移时，我们的结果将通过将我们的结果与障碍问题理论相结合来确定自由边界的规律性。通常，当源和漂移都平滑时，我们证明该解决方案是非分级的，表明自由横向的规律性较高。
In this paper we study the regularity property of Hele-Shaw flow, where source and drift are present in the evolution. More specifically we consider Hölder continuous source and Lipschitz continuous drift. We show that if the free boundary of the solution is locally close to a Lipschitz graph, then it is indeed Lipschitz, given that the Lipschitz constant is small. When there is no drift, our result establishes $C^{1,γ}$ regularity of the free boundary by combining our result with the obstacle problem theory. In general, when the source and drift are both smooth, we prove that the solution is non-degenerate, indicating higher regularity of the free boudary.
