Related papers: The Nikolaevskiy equation with dispersion
The purpose of this paper is to prove that, for a large class of nonlinear evolution equations known as scalar viscous balance laws, the spectral (linear) instability condition of periodic traveling wave solutions implies their orbital…
A model of fully developed turbulence of a compressible fluid is briefly reviewed. It is assumed that fluid dynamics is governed by a stochastic version of Navier-Stokes equation. We show how corresponding field theoretic-model can be…
The features of turbulence modulation produced by a heavy loaded suspension of small solid particles or liquid droplets are discussed by using a physically-based regularisation of particle-fluid interactions. The approach allows a robust…
A simple model of wave-particle interaction is studied in its self-consistent form, that is, where the particles are allowed to feedback on the waves dynamics. We focus on the configurations of locked solutions (equilibria) and how the…
The first well founded perturbation theory for classical solid systems is presented. Theoretical approaches to thermodynamic and structural properties of the hard-sphere solid provide us with the reference system. The traditional…
We propose as a generalization of an idea of Ruelle to describe turbulent fluid flow a chaotic hypothesis for reversible dissipative many particle systems in nonequilibrium stationary states in general. This implies an extension of the…
This PhD thesis is devoted to deterministic study of the turbulence in the Navier- Stokes equations. The thesis is divided in four independent chapters.The first chapter involves a rigorous discussion about the energy's dissipation law,…
We study the spectral stability of smooth, small-amplitude periodic traveling wave solutions of the Novikov equation, which is a Camassa-Holm type equation with cubic nonlinearities. Specifically, we investigate the…
Wave turbulence describes the long-time statistical behavior of out-of-equilibrium systems composed of weakly interacting waves. Non-Hermitian media ranging from open quantum systems to active materials can sustain wave propagation in…
The Hamiltonian formulation of the water wave problem due to Zakharov, and the reduced Zakharov equation derived therefrom, have great utility in understanding and modelling water waves. Here we set out to review the cubic Zakharov equation…
The defining feature of chaos is its hypersensitivity to small perturbations. However, we report a stability of branched flow against large perturbations where the classical trajectories are chaotic, showing that strong perturbations are…
The minimalist approach in the study of perturbations in fluid dynamics and magnetohydrodynamics involves describing their evolution in the linear regime using a single first-order ordinary differential equation, dubbed principal equation.…
Scattered disk objects (SDOs) are distant minor bodies that orbit the sun on highly eccentric orbits, frequently with perhelia near Neptune's orbit. Gravitational perturbations due to Neptune frequently lead to chaotic dynamics, with the…
We establish long-time and large-data existence of a suitable weak solution to three-dimensional internal unsteady flows described by Kolmogorov's two-equation model of turbulence. The governing system of equations is completed by initial…
A new statistical field-theory model of isotropic turbulence is introduced. The model renormalizes the effects of turbulent stresses into a velocity-gradient-dependent random force. The model is well-defined within the context of the…
In this paper, we establish a new criterion for the orbital stability of periodic waves related to a general class of regularized dispersive equations. More specifically, we present sufficient conditions for the stability without knowing…
Intrinsic instability of trajectories characterizes chaotic dynamical systems. We report here that trajectories can exhibit a surprisingly high degree of stability, over a very long time, in a chaotic dynamical system. We provide a detailed…
Model of laminated wave turbulence allows to study statistical and discrete layers of turbulence in the frame of the same model. Statistical layer is described by Zakharov-Kolmogorov energy spectra in the case of irrational enough…
The slider-block Burridge-Knopoff model with the Coulomb friction law is studied as an excitable medium. It is shown that in the continuum limit the system admits solutions in the form of the self-sustained shock waves traveling with…
In this visualisation the instantaneous local velocity is expressed in terms of four components to capture the development of and interactions between coherent structures in turbulent flows. It is then possible to isolate the terms linked…