2021/08/20 by Philippe Laurençot, Laurençot, Philippe, Bogdan–Vasile Matioc +1
Engineering · Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Fluid Dynamics and Thin Films #Navier-Stokes equation solutions #Nonlinear Partial Differential Equations
paper · doi:10.48550/arxiv.2108.09032
openalex publication_date 2021/08/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The singular limit of the thin film Muskat problem is performed when the density (and possibly the viscosity) of the lighter fluid vanishes and the porous medium equation is identified as the limit problem. In particular, the height of the denser fluid is shown to converge towards the solution to the porous medium equation and an explicit rate for this convergence is provided in space dimension d ≤ 4. Moreover, the limit of the height of the lighter fluid is determined in a certain regime and is given by the corresponding initial condition.