Duchon-Robert solutions for the Rayleigh-Taylor and Muskat problems

Abstract

We construct analytic solutions to the Euler equations with an interface between two fluids, extending work of Duchon and Robert. We also show that the estimates of Duchon and Robert yield global analytic solutions to the Muskat problem with small initial data.

18 pages. To appear, J. Diff. Eqns

References in corpus (2)

• On the global existence for the Muskat problem
• Mathematics for 2d Interfaces

Cited by in corpus (5)

• Absence of splash singularities for SQG sharp fronts and the Muskat problem
• On the Muskat problem: global in time results in 2D and 3D
• On The Muskat Problem With Viscosity Jump: Global In Time Results
• Large Time Decay Estimates for the Muskat Equation
• Splash singularities for the one-phase Muskat problem in stable regimes