论文标题
在关键的Sobolev空间中，全球三维麝香问题的全球适应性
Global well-posedness for the three dimensional Muskat problem in the critical Sobolev space
论文作者
论文摘要
我们证明，在关键的Sobolev空间中，3D稳定的Muskat问题在全球范围内均得到充分措施。因此，这使Lipschitz半按任意大。证明是基于3D Muskat问题的新配方，该问题允许捕获问题的隐藏振荡性质。后一种公式允许证明$ \ dot h^{2} $ {\ emph {a priori}}估计。在文献中，3D Muskat问题的所有已知全球存在结果都是针对小斜坡（小于1）。这是第一个用于3D稳定Muskat问题的任意大斜率定理。
We prove that the 3D stable Muskat problem is globally well-posed in the critical Sobolev space $\dot H^2 \cap \dot W^{1,\infty}$ provided that the semi-norm $\Vert f_0 \Vert_{\dot H^{2}}$ is small enough. Consequently, this allows the Lipschitz semi-norm to be arbitrarily large. The proof is based on a new formulation of the 3D Muskat problem that allows to capture the hidden oscillatory nature of the problem. The latter formulation allows to prove the $\dot H^{2}$ {\emph{a priori}} estimates. In the literature, all the known global existence results for the 3D Muskat problem are for small slopes (less than 1). This is the first arbitrary large slope theorem for the 3D stable Muskat problem.
