A remark on the two dimensional water wave problem with surface tension

@article{Shao2017ARO,
  title={A remark on the two dimensional water wave problem with surface tension},
  author={Shuanglin Shao and Hsi-Wei Shih},
  journal={Journal of Differential Equations},
  year={2017}
}
2 Citations

Angled crested type water waves with surface tension II: Zero surface tension limit

This is the second paper in a series of papers analyzing angled crested type water waves with surface tension. We consider the 2D capillary gravity water wave equation and assume that the fluid is

Angled Crested Like Water Waves with Surface Tension: Wellposedness of the Problem

  • S. Agrawal
  • Mathematics
    Communications in Mathematical Physics
  • 2021
We consider the capillary–gravity water wave equation in two dimensions. We assume that the fluid is inviscid, incompressible, irrotational and the air density is zero. We construct an energy

References

SHOWING 1-10 OF 20 REFERENCES

The Zero Surface Tension Limit of Two-Dimensional Water Waves

We consider two‐dimensional water waves of infinite depth, periodic in the horizontal direction. It has been proven by Wu (in the slightly different nonperiodic setting) that solutions to this

The zero surface tension limit of three-dimensional water waves

We establish that the limit of the water wave with surface tension, as surface tension vanishes, is the water wave without surface tension. The main tool is an energy estimate which is uniform in the

Well-posedness in Sobolev spaces of the full water wave problem in 2-D

Abstract. We consider the motion of the interface of 2-D irrotational, incompressible, inviscid water wave, with air above water and surface tension zero. We show that the interface is always not

Generalized vortex methods for free-surface flow problems

The motion of free surfaces in incompressible, irrotational, inviscid layered flows is studied by evolution equations for the position of the free surfaces and appropriate dipole (vortex) and source

Global wellposedness of the 3-D full water wave problem

We consider the problem of global in time existence and uniqueness of solutions of the 3-D infinite depth full water wave problem, in the setting that the interface tends to the horizontal plane, the

Well-Posedness of Vortex Sheets with Surface Tension

For the initial value problem for vortex sheets with surface tension with sufficiently smooth data, it is proved that solutions exist locally in time, are unique, and depend continuously on the initial data.

Well-posedness in Sobolev spaces of the full water wave problem in 3-D

We consider the motion of the interface separating an inviscid, incompressible, irrotational fluid from a region of zero density in three-dimensional space; we assume that the fluid region is below

Well-posedness of 3D vortex sheets with surface tension

We prove well-posedness for the initial value problem for a vortex sheet in 3D fluids, in the presence of surface tension. We first reformulate the problem by making a favorable choice of variables

Removing the stiffness from interfacial flows with surface tension

A new formulation and new methods are presented for computing the motion of fluid interfaces with surface tension in two-dimensional, irrotational, and incompressible fluids. Through the

The long-time motion of vortex sheets with surface tension

We study numerically the simplest model of two incompressible, immiscible fluids shearing past one another. The fluids are two-dimensional, inviscid, irrotational, density matched, and separated by a