相关论文: Scattering Amplitudes and the Navier-Stokes Equati…
We study scattering equations and formulas for tree amplitudes of various theories in four dimensions, in terms of spinor helicity variables and on-shell superspace for supersymmetric theories. As originally obtained in Witten's twistor…
The statistical properties of a scalar field advected by the non-intermittent Navier-Stokes flow arising from a two-dimensional inverse energy cascade are investigated. The universality properties of the scalar field are directly probed by…
We consider the motion of an axisymmetric column of Navier-Stokes fluid with a free surface. Due to surface tension, the thickness of the fluid neck goes to zero in finite time. After the singularity, the fluid consists of two halves, which…
We consider the compressible three dimensional Navier Stokes and Euler equations. In a suitable regime of barotropic laws, we construct a set of finite energy smooth initial data for which the corresponding solutions to both equations…
We show by explicit construction that for every solution of the incompressible Navier-Stokes equation in $p+1$ dimensions, there is a uniquely associated "dual" solution of the vacuum Einstein equations in $p+2$ dimensions. The dual…
The Navier--Stokes equations for incompressible flows past a two--dimensional sphere are considered in this article. The existence of an inertial form of the equations is established. Furthermore for the first time for fluid equations, we…
Using the example of such a complicated problem as the Cauchy problem for the Navier-Stokes equation, we show how the Poincar\'e-Riemann-Hilbert boundary value problem enables us to construct effective estimates of solutions for this case.…
The scattering equations relate massless scattering kinematics to marked points on a Riemann sphere, and underpin remarkable formulae for the full tree-level S-matrices of many interesting QFTs, including cubic biadjoint scalars, Yang-Mills…
We review the properties of the nonlinearly dispersive Navier-Stokes-alpha (NS-alpha) model of incompressible fluid turbulence -- also called the viscous Camassa-Holm equations and the LANS equations in the literature. We first re-derive…
We use the general exact solution of the Cauchy problem for the compressible Euler vortex equation in unbounded space which was obtained earlier (S.G.Chefranov, Sov. Phys. Dokl., 36, 286, 1991). This solution loses its smoothness in finite…
We employ a scalar model to exemplify the use of contour deformations when solving Lorentz-invariant integral equations for scattering amplitudes. In particular, we calculate the onshell 2 -> 2 scattering amplitude for the scalar system.…
Advances in scattering amplitudes have exposed previously-hidden color-kinematics and double-copy structures in theories ranging from gauge and gravity theories to effective field theories such as chiral perturbation theory and the…
We develop mathematical methods which allow us to study asymptotic properties of solutions to the three dimensional Navier-Stokes system for incompressible fluid in the whole three dimensional space. We deal either with the Cauchy problem…
Recently, a non-abelian generalisation of the Navier-Stokes equation that exhibits a manifest duality between colour and kinematics has been proposed by Cheung and Mangan. In this paper, we offer a new perspective on the double copy…
The full compressible Navier-Stokes system describing the motion of a viscous, compressible, heat-conductive, and Newtonian polytropic fluid is studied in a three-dimensional simply connected bounded domain with smooth boundary having a…
We study the initial-boundary value problem of the Navier-Stokes equations for incompressible fluids in a domain in $\R^3$ with compact and smooth boundary, subject to the kinematic and Navier boundary conditions. We first reformulate the…
In this paper, we study the scattering amplitudes and soft theorems for the sigma models with two scalars. We show that if the particles are Goldstone bosons, then you necessarily get Adler zero with no possibility for non-trivial soft…
Loosely speaking, the Navier-Stokes-$\alpha$ model and the Navier-Stokes equations differ by a spatial filtration parametrized by a scale denoted $\alpha$. Starting from a strong two-dimensional solution to the Navier-Stokes-$\alpha$ model…
In this thesis we present a study of the computation of classical observables in gauge theories and gravity directly from scattering amplitudes. In particular, we discuss the direct application of modern amplitude techniques in the one, and…
We prove that soft theorems uniquely fix scattering amplitudes in a wide range of theories, including Yang-Mills, gravity, the non-linear sigma model, Dirac-Born-Infeld, dilaton effective theories, extended theories like NLSM$\oplus \phi^3$…