Related papers: A Novel Method for Generating 3D Hydrodynamic Cons…
We consider free surface dynamics of a two-dimensional incompressible fluid with odd viscosity. The odd viscosity is a peculiar part of the viscosity tensor which does not result in dissipation and is allowed when parity symmetry is broken.…
We develop structure-preserving numerical methods for the Serre-Green-Naghdi equations, a model for weakly dispersive free-surface waves. We consider both the classical form, requiring the inversion of a non-linear elliptic operator, and a…
We present a conservation formulation and a numerical algorithm for the reduced-gravity shallow-water equations on a beta plane, subjected to a constant wind forcing that leads to the formation of double-gyre circulation in a closed ocean…
A number of astrophysical scenarios possess and preserve an overall cylindrical symmetry also when undergoing a catastrophic and nonlinear evolution. Exploiting such a symmetry, these processes can be studied through numerical-relativity…
In this paper we derive a new formulation of the water waves equations with vorticity that generalizes the well-known Zalkarov-Craig-Sulem formulation used in the irrotational case. We prove the local well-posedness of this formulation, and…
We present an extension of the Piecewise Parabolic Method to special relativistic fluid dynamics in multidimensions. The scheme is conservative, dimensionally unsplit, and suitable for a general equation of state. Temporal evolution is…
In this paper we prove global regularity for the full water waves system in 3 dimensions for small data, under the influence of both gravity and surface tension. This problem presents essential difficulties which were absent in all of the…
We are interested in a nonlocal conservation law which describes the morphodynamics of sand dunes sheared by a fluid flow, recently proposed by Andrew C. Fowler. We prove that constant solutions of Fowler's equation are non-linearly…
We review recent progress on the long-time regularity of solutions of the Cauchy problem for the water waves equations, in two and three dimensions. We begin by introducing the free boundary Euler equations and discussing the local…
It is shown how a complete set of hydrodynamic equations describing an unsteady three-dimensional viscous flow nearby a solid body, can be reduced to a closed system of surface equations using the method of dimension reduction of…
The notions of generating sets of conservation laws of systems of differential equations with respect to symmetry groups and equivalence groups are introduced and applied. This allows us to generalize essentially the procedure of finding…
In this paper we discuss energy conservation issues related to the numerical solution of the nonlinear wave equation. As is well known, this problem can be cast as a Hamiltonian system that may be autonomous or not, depending on the…
The motion of an incompressible fluid in Lagrangian coordinates involves infinitely many symmetries generated by the left Lie algebra of group of volume preserving diffeomorphisms of the three dimensional domain occupied by the fluid.…
We develop a purely hydrodynamic formalism to describe collisional, anisotropic instabilities in a relativistic plasma, that are usually described with kinetic theory tools. Our main motivation is the fact that coarse-grained models of high…
This paper presents recent work on connections between symmetries and conservation laws. After reviewing Noether's theorem and its limitations, we present the Direct Construction Method to show how to find directly the conservation laws for…
We consider the hydrodynamic regime of theories with quantum anomalies for global currents. We show that a hitherto discarded term in the conserve current is not only allowed by symmetries, but is in fact required by triangle anomalies and…
A novel structure-preserving numerical method to solve random hyperbolic systems of conservation laws is presented. The method uses a concept of generalized, measure-valued solutions to random conservation laws. This yields a linear partial…
A fluid described by an Abelian Chern-Simons action principle in 4+1 dimensions is considered. Letting 3+1 dimensions correspond to the usual space and time, and assuming the fields to be independent of the fifth coordinate, the free theory…
We prove global existence of solutions to the initial value problem for a third order dispersive flow into compact locally Hermitian symmetric spaces. The equation we consider generalizes two-sphere-valued completely integrable systems…
We consider the propagation of linear gravity waves on the free surface of steady, axisymmetric flows with purely azimuthal velocity. We propose a two-dimensional set of governing equations for surface waves valid in the deep-water limit.…