论文标题
3D Muskat问题的最终正规化：有限时间的Lipschitz意味着全球存在
Eventual regularization for the 3D Muskat problem: Lipschitz for finite time implies global existence
论文作者
论文摘要
我们表明，对于任何固定的Lipschitz常量$ L $，有一个时间$ t^*<\ infty $仅取决于$ l $，以便如果$ f：[0，t^*] \ times \ times \ times \ times \ athbb {r}^{2}^{2} \ to [0,1] $是与稳定的muskat $ | nabla的经典解决方案f || _ {l^\ infty} \ leq l $，然后$ f $唯一地扩展到一直定义的经典解决方案。我们的证明是简短，定量和明确的。
We show that for any fixed Lipschitz constant $L$, there is a time $T^*<\infty$ depending only on $L$ such that if $f:[0,T^*]\times \mathbb{R}^{2}\to [0,1]$ is a classical solution of the stable Muskat problem with $||\nabla_x f||_{L^\infty}\leq L$, then $f$ extends uniquely to a classical solution defined for all time. Our proof is short, quantitative, and explicit.
