相关论文: Wave turbulence and the kinetic equation beyond le…

A nonlinear Schrodinger equation arising from light propagation down an inhomogeneous medium is considered. The inhomogeneity is reflected through a non-uniform coefficient of the non-linear term in the equation. In particular, a…

We investigate the properties of standing waves to a nonlinear Schr\"odinger equation with inverse-square potential on the half-line. We first establish the existence of standing waves. Then, by a variational characterization of the ground…

Motivated by the Onsager statistical mechanics description of turbulent Euler flows with point singularities, we obtain a Harnack-type inequality for sequences of solutions of the following perturbed Liouville equation,…

The problem of response of nonequilibrium systems is currently under intense investigation. We propose a general method of solution of the Liouville Equation for thermostatted particle systems subjected to external forces which retains only…

Weak Wave Turbulence is a powerful theory to predict statistical observables of diverse relevant physical phenomena, such as ocean waves, magnetohydrodynamics and nonlinear optics. The theory is based upon an asymptotic closure permitted in…

Intensity distributions of linear wave fields are, in the high frequency limit, often approximated in terms of flow or transport equations in phase space. Common techniques for solving the flow equations for both time dependent and…

In this work, we discuss a situation which could lead to both wave turbulence and collective behavior kinetic equations. The wave turbulence kinetic models appear in the kinetic limit when the wave equations have local differential…

Lower-branch traveling waves and equilibria computed in pipe flow and other shear flows appear intermediate between turbulent and laminar motions. We take a step towards connecting these lower-branch solutions to transition by deriving a…

A Hamiltonian model for the propagation of internal water waves interacting with surface waves, a current and an uneven bottom is examined. Using the so-called Dirichlet-Neumann operators, the water wave system is expressed in the…

In this paper, we study local well-posedness and orbital stability of standing waves for a singularly perturbed one-dimensional nonlinear Klein-Gordon equation. We first establish local well-posedness of the Cauchy problem by a fixed point…

The kinetic wave equation arises in wave turbulence to describe the Fourier spectrum of solutions to the cubic Schroedinger equation. The equation has two Kolmogorov-Zakharov steady states corresponding to out-of-equilibrium cascades…

Starting from the von Neumann-Maxwell equations for the Wigner quasi-probability distribution and for the self-consistent electric field, the quantum analog of the classical single-wave model has been derived. The linear stability of the…

This article is devoted to forward and inverse problems associated with time-independent semilinear nonlocal wave equations. We first establish comprehensive well-posedness results for some semilinear nonlocal wave equations. The main…

We consider the four waves spatial homogeneous kinetic equation arising in wave turbulence theory. We study the long-time behaviour and existence of solutions around the Rayleigh-Jeans equilibrium solutions. For cut-off'd frequencies, we…

We consider stationary, forced, imbalanced, or cross-helical MHD Alfvenic turbulence where the waves traveling in one direction have higher amplitudes than the opposite waves. This paper is dedicated to so-called strong turbulence, which…

Liouville conformal field theory describes a random geometry that fluctuates around a deterministic one: the unique solution of the problem of finding, within a given conformal class, a Riemannian metric with prescribed scalar and geodesic…

This paper is concerned with the processes of spatial propagation and penetration of turbulence from the regions where it is locally excited into initially laminar regions. The phenomenon has come to be known as "turbulence spreading" and…

Active turbulence is a paradigmatic and fascinating example of self-organized motion at large scales occurring in active matter. We employ massive hydrodynamic simulations of suspensions of resolved model microswimmers to tackle the…

Wilton ripples are a type of periodic traveling wave solution of the full water wave problem incorporating the effects of surface tension. They are characterized by a resonance phenomenon that alters the order at which the resonant harmonic…

In this article, a perturbation theory of the compressible Navier-Stokes equations in $\mathbb{R}^n$ $(n \geq 3)$ is studied to investigate decay estimate of solutions around a non-constant state. As a concrete problem, stability is…