We prove the existence of mixing solutions of the incompressible porous media equation for all Muskat type \(H^5\) initial data in the fully unstable regime. The proof combines convex integration, contour dynamics and a basic calculus for non smooth semiclassical type pseudodifferential operators which is developed.

中文翻译：

---

马斯喀特问题的混合解决方案

对于完全不稳定状态下的所有Muskat类型\（H ^ 5 \）初始数据，我们证明了不可压缩多孔介质方程的混合解的存在。该证明结合了凸积分，轮廓动力学和针对非光滑半经典类型伪微分算子的基本演算。