Non-splat singularity for the one-phase Muskat problem

2014/09/09 by Diego Córdoba, Córdoba, Diego, Tania Pernas-Castaño +1
Earth and Planetary Sciences · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Ocean Waves and Remote Sensing

paper · pdf · doi:10.48550/arxiv.1409.2483

openalex publication_date 2014/09/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For the water waves equations, the existence of splat singularities has been shown in [3], i.e., the interface self-intersects along an arc in finite time. The aim of this paper is to show the absence of splat singularities for the incompressible fluid dynamics in porous media.

Citations

• The penetration of a fluid into a porous medium or Hele-Shaw cell containing a more viscous liquid
• Well-posedness of the Muskat problem with H² initial data

Related

• Splash singularities for the one-phase Muskat problem in stable regimes
• Finite time singularities for the free boundary incompressible Euler equations
• Rigidity of Acute Angled Corners for One Phase Muskat Interfaces
• Singularity Formation in the Incompressible Porous Medium Equation without Boundary Mass
• Rayleigh-Taylor breakdown for the Muskat problem with applications to water waves