Related papers: Euler Equation on a Rotating Surface
This paper is devoted to the stabilization of the incompressible Euler equation with free surface. We study the damping of two-dimensional gravity waves by an absorbing beach where the water-wave energy is dissipated by using the variations…
We present a symmetry result regarding stationary solutions of the 2D Euler equations in a disk. We prove that in a disk, a steady flow with only one stagnation point and tangential boundary conditions is a circular flow, which confirms a…
Causal variational principles, which are the analytic core of the physical theory of causal fermion systems, are found to have an underlying Hamiltonian structure, giving a formulation of the dynamics in terms of physical fields in…
In Part I, we construct a class of examples of initial velocities for which the unique solution to the Euler equations in the plane has an associated flow map that lies in no Holder space of positive exponent for any positive time. In Part…
Oscillatons are spherically symmetric solutions to the Einstein Klein Gordon (EKG) equations for soliton stars made of real time dependent scalar fields. These equations are non singular and satisfy flatness conditions asymptotically with…
A basis set expansion is performed to find the eigenvalues and wave functions for an electron on a toroidal surface $T^2$ subject to a constant magnetic field in an arbitrary direction. The evolution of several low-lying states as a…
We consider the incompressible Euler equations in $R^2$ when the initial vorticity is bounded, radially symmetric and non-increasing in the radial direction. Such a radial distribution is stationary, and we show that the monotonicity…
Using fully three-dimensional hydrodynamic simulations, we investigate the effect of the Coriolis force on the hydrodynamic and observable properties of colliding wind binary systems. To make the calculations tractable, we assume adiabatic,…
We start by surveying the planar point vortex motion of the Euler equations in the whole plane, half-plane and quadrant. Then we go on to prove non-collision property of 2-vortex system by using the explicit form of orbits of 2-vortex…
We present dynamic equations for two dimensional closed surfaces and analytically solve it for some simplified cases. We derive final equations for surface normal motions by two different ways. The solution of the equations of motions in…
We investigate the nonlinear effects of uniform rotation on the Parker instability in an exponentially-stratified disk through high-resolution simulations. During the linear stage, the speed of gas motion is subsonic and the evolution with…
Flexibility and rigidity properties of steady (time-independent) solutions of the Euler, Boussinesq and Magnetohydrostatic equations are investigated. Specifically, certain Liouville-type theorems are established which show that suitable…
The motion of two planets around a Sun-like star under the combined effects of mutual interaction and tidal dissipation is investigated. The secular behaviour of the system is analyzed using two different approaches. First, we solve the…
The dynamics along the particle trajectories for the 3D axisymmetric Euler equations in an infinite cylinder are considered. It is shown that if the inflow-outflow is highly oscillating in time, the corresponding Euler flow cannot keep the…
We prove that the 3-D compressible Euler equations with surface tension along the moving free-boundary are well-posed. Specifically, we consider isentropic dynamics and consider an equation of state, modeling a liquid, given by Courant and…
We obtain a general sufficient condition on the geometry of possibly singular planar domains that guarantees global uniqueness for any weak solution to the Euler equations on them whose vorticity is bounded and initially constant near the…
Several alternative methods for description of interaction between rotation and vibration are compared and contrasted using hyper-spherical coordinates for a triatomic molecule. These methods differ by the choice of z-axis and by the…
The time dependent Schrodinger equation inclusive of curvature effects is developed for a spinless electron constrained to motion on a toroidal surface and subjected to circularly polarized and linearly polarized waves in the microwave…
We prove that the 3-D free-surface incompressible Euler equations with regular initial geometries and velocity fields have solutions which can form a finite-time "splash" (or "splat") singularity first introduced in [9], wherein the…
On any closed Riemannian 3-manifold which is not a torus bundle, every nonvanishing analytic solution of the stationary Euler equations has a periodic trajectory. This result is originally due to A. Rechtman (arXiv:0904.2719) and K.…