Related papers: Interface evolution: water waves in 2-D
We consider an interface with surface tension that separates a perfectly conducting inviscid fluid from a vacuum. The fluid flow is governed by the equations of ideal compressible magnetohydrodynamics (MHD), while the electric and magnetic…
We consider the Cauchy problem for the 2D gravity water wave equation. Recently Wu \cite{Wu15, Wu18} proved the local well-posedness of the equation in a regime which allows interfaces with angled crests as initial data. In this work we…
Consider a viscous fluid of finite depth below the air. In the absence of the surface tension effect at the air-fluid interface, the long time behavior of a free surface with small amplitude has been an intriguing question since the work of…
We consider the initial value problem for a nonlinear shallow water model in horizontal dimension d = 2 and in the presence of a fixed partially immersed solid body on the water surface. We assume that the bottom of the solid body is the…
We establish that solitary stationary waves in three dimensional viscous incompressible fluids are a generic phenomenon and that every such solution is a vanishing wave-speed limit along a one parameter family of traveling waves. The…
We study the immersed boundary problem in 2-D. It models a 1-D elastic closed string immersed and moving in a fluid that fills the entire plane, where the fluid motion is governed by the 2-D incompressible Navier-Stokes equation with a…
We address a free boundary model for the compressible Euler equations where the free boundary, which is elastic, evolves according to a weakly damped fourth order hyperbolic equation forced by the fluid pressure. This system captures the…
The two dimensional gravity water wave problem concerns the motion of an incompressible fluid occupying half the 2D space and flowing under its own gravity. In this paper we study long-term regularity of solutions evolving from small but…
Isothermal compressible two-phase flows in a capillary are modeled with and without phase transition in the presence of gravity, employing Darcy's law for the velocity field. It is shown that the resulting systems are thermodynamically…
In this dissertation two-dimensional buoyancy-driven flows are investigated. While usually the Navier-Stokes equations are equipped with no-slip boundary conditions here we focus on the Navier-slip conditions that, depending on the system…
In fluid dynamics, an interface splash singularity occurs when a locally smooth interface self-intersects in finite time. We prove that for $d$-dimensional flows, $d=2$ or $3$, the free-surface of a viscous water wave, modeled by the…
In this work we study the evolution of the interface between two different fluids in two concentric cylinders when the velocity is given by the Navier-Stokes equation and one of the fluids is thin. We present a formal asymptotic derivation…
We consider the free boundary problem for the incompressible elastodynamics equations. At the free boundary moving with the velocity of the fluid particles the columns of the deformation gradient are tangent to the boundary and the pressure…
A two-dimensional water wave system is examined consisting of two discrete incompressible fluid domains separated by a free common interface. In a geophysical context this is a model of an internal wave, formed at a pycnocline or…
We are interested in the system of gravity water waves equations without surface tension. Our purpose is to study the optimal regularity thresholds for the initial conditions. In terms of Sobolev embeddings, the initial surfaces we consider…
Walter Craig's seminal works on the water-waves problem established the importance of several exact identities: Zakharov's hamiltonian formulation, shape derivative formula for the Dirichlet-to-Neumann operator, normal forms…
Two-dimensional single-mode Rayleigh-Taylor Instability (RTI) is simulated using an accurate and robust front-tracking/ghost-fluid method (FT/GFM) with high-order weighted essentially non-oscillatory (WENO) scheme. We compare our numerical…
Layzer's approximation method for investigation of two fluid interface structures associated with Rayleigh Taylor instability for arbitrary Atwood number is extended with the inclusion of second harmonic mode leaving out the zeroth harmonic…
We study the local well-posedness for an interface with surface tension that separates a perfectly conducting inviscid fluid from a vacuum. The fluid flow is governed by the equations of three-dimensional ideal compressible…
The role of instability in the growth of a 2D, temporally evolving, `turbulent' free shear layer is analyzed using vortex-gas simulations that condense all dynamics into the kinematics of the Biot-Savart relation. The initial evolution of…