Related papers: Pointwise Behavior of the Linearized Boltzmann Equ…

We study the time decay estimates for the linearized Landau equation on torus when the initial perturbation is not necessarily smooth. Our result reveals the kinetic and fluid aspects of the equation. We design a Picard-type iteration and…

This paper considers a system of Boltzmann equations modelling the mixture of monatomic and polyatomic gases in an $L^{2}-L^{\infty}$ perturbation theory around global modified Maxwellians accounting for the internal energy of the mixture…

Consider the cubic nonlinear Schr\"odinger equation set on a d-dimensional torus, with data whose Fourier coefficients have phases which are uniformly distributed and independent. We show that, on average, the evolution of the moduli of the…

A spatially-periodic longitudinal wave is considered in relativistic dissipative hydrodynamics. At sufficiently small wave amplitudes, an analytic solution is obtained in the linearised limit of the macroscopic conservation equations within…

In the dynamics generated by the suspension bridge equation, traveling waves are an essential feature. The existing literature focuses primarily on the idealized one-dimensional case, while traveling structures in two spatial dimensions…

We study the Boltzmann equation with hard sphere in a near-equilibrium setting. The initial data is compactly supported in the space variable and has a polynomial tail in the microscopic velocity. We show that the solution can be decomposed…

A quadrature-based finite-difference lattice Boltzmann model is developed that is suitable for simulating relativistic flows of massless particles. We briefly review the relativistc Boltzmann equation and present our model. The quadrature…

A non-linear model associated with a Landau-Ginzburg-like behavior in mean field approximation forecasts phase transition waves and solitary kinks near the critical point. The behavior of isothermal waves is different of the one of…

The observation of fluid-like behavior in nucleus-nucleus, proton-nucleus and high-multiplicity proton-proton collisions motivates systematic studies of how different measurements approach their fluid-dynamic limit. We have developed…

The nonlinear Schr\"odinger equation in the weakly nonlinear regime with random Gaussian fields as initial data is considered. The problem is set on the torus in any dimension greater than two. A conjecture in statistical physics is that…

We consider the two-dimensional water-wave problem with a general non-zero vorticity field in a fluid volume with a flat bed and a free surface. The nonlinear equations of motion for the chosen surface and volume variables are expressed…

The linearized Boltzmann equation is considered to describe small spatial perturbations of the homogeneous cooling state. The corresponding macroscopic balance equations for the density, temperature, and flow velocity are derived from it as…

In this work we revisit a classical problem of traveling waves in a damped Frenkel-Kontorova lattice driven by a constant external force. We compute these solutions as fixed points of a nonlinear map and obtain the corresponding kinetic…

We use the extended relaxation time approximation for the collision kernel, which incorporates a particle-energy dependent relaxation time, to derive second-order viscous hydrodynamics from the Boltzmann equation for a system of massless…

In this paper we apply the lattice-Boltzmann method and an extension to particle suspensions as introduced by Ladd et al. to study transport phenomena and structuring effects of particles suspended in a fluid near sheared solid walls. We…

We study the waves at the interface between two thin horizontal layers of immiscible fluids subject to high-frequency horizontal vibrations. Previously, the variational principle for energy functional, which can be adopted for treatment of…

We present experimental results on hydrothermal traveling-waves dynamics in long and narrow 1D channels. The onset of primary traveling-wave patterns is briefly presented for different fluid heights and for annular or bounded channels,…

This paper deals with the dead-water phenomenon, which occurs when a ship sails in a stratified fluid, and experiences an important drag due to waves below the surface. More generally, we study the generation of internal waves by a…

This paper considers properties of nonlinear waves and solitons of Korteweg-de Vries equation in the presence of external perturbation. For time-periodic hamiltonian perturbation the width of the stochastic layer is calculated. The…

We develop and implement a novel lattice Boltzmann scheme to study multicomponent flows on curved surfaces, coupling the continuity and Navier-Stokes equations with the Cahn-Hilliard equation to track the evolution of the binary fluid…