2026/03/31 by Qasim Khan, Anthony Suen, Bao Quoc Tang
Mathematics · #math.AP #msc:76D03 #msc:35Q35 #msc:76W05
arxiv created 2026/08/04 · arxiv updated 2026/08/05
We address a generalised three-dimensional α-Muskat model that comes from the fluid interface problem given by two incompressible fluids with different densities in the stable regime. We establish local-in-time wellposedness when α∈[0,1) and also prove global-in-time existence for strong solutions when α∈[0,(1)/(2)) with initial data controlled by explicit constants. We obtain maximum principles for the L∞-norms of both the solutions and their gradients, and we further acquire the corresponding decay rates of these L∞-norms. Finally, some convergence results for strong solutions as α→0+ are also proved.