论文标题
3D Muskat问题的全球良好性与中等坡度
Global wellposedness for the 3D Muskat problem with medium size slope
论文作者
论文摘要
每当初始接口具有额定值的生长和斜率$ || \ nabla_x f_0 || _ {l^\ infty} <5^{ - 1/2} $时，我们证明了稳定制度中3D Muskat问题的全球经典解决方案的存在和独特性。我们在这些假设下表明，该方程在根本上是抛物面，满足了比较原理。应用连续性技术的模量，我们表明粗糙的初始数据立即变成$ c^{1,1} $，曲率衰减如$ o（t^{ - 1}）$。
We prove the existence and uniqueness of global, classical solutions to the 3D Muskat problem in the stable regime whenever the initial interface has sublinear growth and slope $||\nabla_x f_0||_{L^\infty}< 5^{-1/2}$. We show under these assumptions that the equation is fundamentally parabolic, satisfying a comparison principle. Applying the modulus of continuity technique, we show that rough initial data instantly becomes $C^{1,1}$ with the curvature decaying like $O(t^{-1})$.
