Add to ORKGAbstract. We show that ”splash ” singularities cannot develop in the case of locally smooth so-lutions of the two-fluid interfaces in two dimensions. More precisely, we show that the scenario of formation of singularities discovered by Castro–Córdoba–Fefferman–Gancedo–Gómez-Serrano [6] in the case of the water waves system, in which the interface remains locally smooth but self-intersects in finite time, is completely prevented in the case of two-fluid interfaces with positive densities. Content
The initial-value problem for the evolution of the interface η(x, t) separating two unbounded, invis...
In this paper, we prove the existence of smooth initial data for the 2D free boundary incompressible...
In light of the question of finite-time blow-up vs. global well-posedness of solutions to problems i...
We show that so-called splash singularities cannot develop in the case of locally smooth solutions o...
We exhibit smooth initial data for the two-dimensional (2D) water-wave equation for which we prove t...
In fluid dynamics, an interface splash singularity occurs when a locally smooth interface s...
In fluid dynamics, an interface splash singularity occurs when a locally smooth interface s...
In fluid dynamics, an interface splash singularity occurs when a locally smooth interface s...
In fluid dynamics, an interface splash singularity occurs when a locally smooth interface s...
The study of linearized interface wave problems for two superposed fluids often involves the conside...
For the water waves equations, the existence of splat singularities has been shown in [3], i.e., the...
The three-dimensional interfacial waves due to a fundamental singularity steadily moving in a system...
The equations of hydrodynamics are nonlinear partial differential equations, so they include the pos...
We prove that there are stationary solutions to the 2D incompressible free boundary Euler equations ...
The initial-value problem for the evolution of the interface η(x, t) separating two unbounded, invis...
The initial-value problem for the evolution of the interface η(x, t) separating two unbounded, invis...
In this paper, we prove the existence of smooth initial data for the 2D free boundary incompressible...
In light of the question of finite-time blow-up vs. global well-posedness of solutions to problems i...
We show that so-called splash singularities cannot develop in the case of locally smooth solutions o...
We exhibit smooth initial data for the two-dimensional (2D) water-wave equation for which we prove t...
In fluid dynamics, an interface splash singularity occurs when a locally smooth interface s...
In fluid dynamics, an interface splash singularity occurs when a locally smooth interface s...
In fluid dynamics, an interface splash singularity occurs when a locally smooth interface s...
In fluid dynamics, an interface splash singularity occurs when a locally smooth interface s...
The study of linearized interface wave problems for two superposed fluids often involves the conside...
For the water waves equations, the existence of splat singularities has been shown in [3], i.e., the...
The three-dimensional interfacial waves due to a fundamental singularity steadily moving in a system...
The equations of hydrodynamics are nonlinear partial differential equations, so they include the pos...
We prove that there are stationary solutions to the 2D incompressible free boundary Euler equations ...
The initial-value problem for the evolution of the interface η(x, t) separating two unbounded, invis...
The initial-value problem for the evolution of the interface η(x, t) separating two unbounded, invis...
In this paper, we prove the existence of smooth initial data for the 2D free boundary incompressible...
In light of the question of finite-time blow-up vs. global well-posedness of solutions to problems i...