The free boundary Euler equations with large surface tension

Abstract

We study the free boundary Euler equations with surface tension in three spatial dimensions, showing that the equations are well-posed if the coefficient of surface tension is positive. Then we prove that under natural assumptions, the solutions of the free boundary motion converge to solutions of the Euler equations in a domain with fixed boundary when the coefficient of surface tension tends to infinity.

to appear in Journal of Differential Equations

References in corpus (2)

• A priori estimates for the motion of a self-gravitating incompressible liquid with free surface boundary
• On a linear problem arising in dynamic boundaries

Cited by in corpus (8)

• Causality and existence of solutions of relativistic viscous fluid dynamics with gravity
• A Regularity Result for the Incompressible Magnetohydrodynamics Equations with Free Surface Boundary
• A Lagrangian Interior Regularity Result for the Incompressible Free Boundary Euler Equation with Surface Tension
• A priori estimates for the free-boundary Euler equations with surface tension in three dimensions
• On the Incompressible Limit for the Compressible Free-Boundary Euler Equations with Surface Tension in the Case of a Liquid
• A priori estimates for the 3D compressible free-boundary Euler equations with surface tension in the case of a liquid
• On the impossibility of finite-time splash singularities for vortex sheets
• On a linear problem arising in dynamic boundaries