## 2 Citations

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

- Mathematics
- 2020

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

- MathematicsCommunications 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

- Mathematics
- 2005

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

- Mathematics
- 2009

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

- Mathematics
- 1997

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

- PhysicsJournal of Fluid Mechanics
- 1982

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

- Mathematics
- 2011

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

- MathematicsSIAM J. Math. Anal.
- 2003

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

- Mathematics
- 1999

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

- Mathematics
- 2007

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

- Mathematics
- 1994

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

- Physics
- 1997

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…