Related papers: GENERIC formulation and small-angle limit for Kine…
The collision of two plane gravitational waves in Einstein's theory of relativity can be described mathematically by a Goursat problem for the hyperbolic Ernst equation in a triangular domain. We use the integrable structure of the Ernst…
The purpose of this paper is to formulate a kinetic theory describing transport properties of electrons in a uniform magnetic field of arbitrary magnitude. Exposing an electronic system to a constant magnetic field quenches its energy bands…
Starting from a stochastic Zakharov-Kuznetsov (ZK) equation on a lattice, the previous work [ST21] by the last two authors gave a derivation of the homogeneous 3-wave kinetic equation at the kinetic limit under very general assumptions: the…
The proper-time method for constructing perturbative dynamical gravitational fields is presented. Using the proper-time method, a perturbative analytical model of gravitational waves against the backdrop of an exact wave solution of…
In rotating stratified flows including in the atmosphere and ocean, inertia-gravity waves (IGWs) often coexist with a geostrophically balanced turbulent flow. Advection and refraction by this flow lead to wave scattering, redistributing IGW…
Internal waves in the ocean interact in triads. Early work emphasized the importance of extreme-scale separated interactions in which two large wavenumber waves interact with one small wavenumber wave. More recent efforts have called this…
We continue here with previous investigations on the global behavior of general type non-linear wave equations for a class of small, scale-invariant initial data. The method is based on the use of a new set of Strichartz estimates for the…
The main purpose of this expository note is to give a short account of the recent developments in mathematical wave kinetic theory. After reviewing the physical theory, we explain the importance of the notion of a scaling law, which…
We prove global in time dispersion for the wave and the Klein-Gordon equation inside the Friedlander domain by taking full advantage of the space-time localization of caustics and a precise estimate of the number of waves that may cross at…
We investigate the properties of a fairly large class of boundary conditions for the linearised Einstein equations in the Riemannian setting, ones which generalise the linearised counterpart of boundary conditions proposed by Anderson.…
We complete the existing literature on the kinetic theory of systems with long-range interactions. Starting from the BBGKY hierarchy, or using projection operator technics or a quasilinear theory, a general kinetic equation can be derived…
1) A wave equation is derived from the kinetic equations governing media with rotational as well as translational degrees of freedom. In this wave the fluctuating quantity is a vector, the bulk spin. The transmission is similar to…
In this study, we develop the generalized Dirac like four-momentum equation for rotating spin-half particles in four-dimensional quaternionic algebra. The generalized quaternionic Dirac equation consists the rotational energy and angular…
The behavior of dynamical system interacting with non-equilibrium medium is investigated. Formally exact kinetic equations are derived for the statistical operator of the dynamical system and the macroscopic parameters of the medium. In the…
A relativistic version of the Kinetic Theory for polyatomic gas is considered and a new hierarchy of moments that takes into account the total energy composed by the rest energy and the energy of the molecular internal modes is presented.…
In this paper, we consider the long-term behavior of some special solutions to the Wave Kinetic Equation (WKE). This equation provides a mesoscopic description of wave systems interacting nonlinearly via the cubic NLS equation. Escobedo and…
New upper and lower limits are given for the number of S-wave bound states yielded by an attractive (monotonic) potential in the context of the Schrodinger or Klein-Gordon equation.
A theory for the characterization of the fourth moment of electromagnetic wave beams is presented in the case when the source is partially coherent. A Gaussian-Schell model is used for the partially coherent random source. The white-noise…
The classical version of the three wave interaction models the creation and destruction of waves; the quantized version models the creation and destruction of particles. The quantum three wave interaction is described and the Bethe Ansatz…
This article provides non-trivial technical ingredients for the article "The quantitative hydrodynamic limit of the Kawasaki dynamics" by the same authors. In that work a quantitative version of the hydrodynamic limit is deduced using a…