Related papers: Boundary observability of gravity water waves
We consider the two-dimensional deep gravity-capillary water waves with point vortices. We first formulate the question in the holomorphic coordinates. Then, we derive an a priori energy estimate for water waves, and show that the water…
Processes of propagation and interaction of nonlinear gravity-capillary waves on the free surface of a deep non-conducting liquid with high dielectric constant under the action of a tangential electric field are numerically simulated. The…
We prove energy estimates for a relativistic free liquid body with sufficiently small fluid velocity in a general Einstein spacetime. These estimates control Sobolev norms of the fluid velocity and enthalpy in the interior as well as…
We investigate the influence of gravitational waves on a freely falling hydrogen atom by analyzing the dynamics of the bound electron described by the Dirac equation in the curved spacetime of a gravitational wave. From this, we derive the…
The main purpose of this paper is to seek a mechanical interpretation of gravitational phenomena. We suppose that the universe may be filled with a kind of fluid which may be called the $\Omega (0)$ substratum. Thus, the inverse-square law…
This paper investigates solitary water waves propagating along the surface of a two-dimensional dielectric fluid with constant vorticity in the presence of an external electric field. We formulate the system as a nonlinear free boundary…
Granular particles vibrated in a fluid have been found to exhibit self-organization with attractive and repulsive interactions between the particles. These interactions have been attributed to the steady streaming flow around oscillating…
We derive an effective gravitational potential, induced by the quantum wavefunction of a physical vacuum of a self-gravitating configuration, while the vacuum itself is viewed as the superfluid described by the logarithmic quantum wave…
The gravitational self-force acting on a particle orbiting a massive central body has thus far been computed for vacuum spacetimes involving a black hole. In this work we continue an ongoing effort to study the self-force in nonvacuum…
We consider the gravity-capillary water waves problem in a domain $\Omega_t \subset \mathbb{T} \times \mathbb{R}$ with substantial geometric features. Namely, we consider a variable bottom, smooth obstacles in the flow and a constant…
In this paper, we consider a free boundary problem of two-phase inviscid incompressible fluid in gravity field. The presence of the gravity field induces novel phenomena that there might be some stagnation points on free surface of the…
We prove local well-posedness for the gravity water waves equations without surface tension, with initial velocity field in $H^s$, $s > \frac{d}{2} + 1 - \mu$, where $\mu = \frac{1}{10}$ in the case $d = 1$ and $\mu = \frac{1}{5}$ in the…
We consider the sloshing problem for an incompressible, inviscid, irrotational fluid in an open container, including effects due to surface tension on the free surface. We restrict ourselves to a constant contact angle and seek…
We consider two-dimensional steady periodic gravity waves on water of finite depth with a prescribed but arbitrary vorticity distribution. The water surface is allowed to be overhanging and no assumptions regarding the absence of stagnation…
Wave resistance is the drag force associated to the emission of waves by a moving disturbance at a fluid free surface. In the case of capillary-gravity waves it undergoes a transition from zero to a finite value as the speed of the…
Cavitation in a liquid moving past a constraint is numerically investigated by means of a free-energy lattice Boltzmann simulation based on the van der Waals equation of state. The fluid is streamed past an obstacle and, depending on the…
We revisit the boundary dynamics of asymptotically flat, three dimensional gravity. The boundary is governed by a momentum conservation equation and an energy conservation equation, which we interpret as fluid equations, following the…
We consider steady three-dimensional gravity-capillary water waves with vorticity propagating on water of finite depth. We prove a variational principle for doubly periodic waves with relative velocities given by Beltrami vector fields,…
The nonlinear dynamics of waves at the sea surface is believed to be ruled by the Weak Turbulence framework. In order to investigate the nonlinear coupling among gravity surface waves, we developed an experiment in the Coriolis facility…
Third-order approximate solutions for surface gravity waves in the finite water depth are studied in the context of potential flow theory. This solution provides explicit expressions for the surface elevation, free-surface velocity…