论文标题
关于Muskat方程的Cauchy问题。 II：关键初始数据
On the Cauchy problem for the Muskat equation. II: Critical initial data
论文作者
论文摘要
我们证明，Muskat方程的Cauchy问题在本地及时在Lipschitz函数的关键空间中的任何初始数据及时及时，并在$ l^2 $中具有三半衍生物。此外，我们证明该解决方案在较小的假设下全球存在。
We prove that the Cauchy problem for the Muskat equation is well-posed locally in time for any initial data in the critical space of Lipschitz functions with three-half derivative in $L^2$. Moreover, we prove that the solution exists globally in time under a smallness assumption.
