Chi-Kun Lin

On some compressible fluid models: Korteweg, lubrication, and shallow water systems

Abstract In this article, we give some mathematical results for an isothermal model of capillary compressible fluids derived by Dunn and Serrin in [1]Dunn JE, Serrin J. On the thermodynamics of interstitial working. Arch Rational Mech Anal. 1985; 88(2):95–133), which can be used as a phase transition model. We consider a periodic domain Ω = T d (d = 2 ou 3) or a strip domain Ω = (0,1) × T d −1. We look at the dependence of the viscosity μ and the capillarity coefficient κwith respect to the density ρ. Depending on the cases we consider, different results are obtained. We prove for instance for a viscosity μ(ρ) = νρ and a surface tension the global existence of weak solutions of the Korteweg system without smallness assumption on the data. This model includes a shallow water model and a lubrication model. We discuss the validity of the result for the shallow water equations since the density is less regular than in the Korteweg case.

Low Mach Number Limit of Viscous Polytropic Flows: Formal Asymptotics in the Periodic Case

This article is devoted to the low Mach number limit of weak solutions to the compressible Navier-Stokes equations for polytropic fluids with periodic boundary conditions and ill-prepared data. We derive formally the equation satisfied by the mean value of the velocity and the equations governing the dynamics of the nonlinear acoustic waves in dimension d = 2 or 3.

On the incompressible limit of the compressible navier-stokes equations

Many interesting problems in classical physics involve the behavior of solutions of nonlinar hyperbolic systems as certain parameter and coefficients becomes infinite. Quite often, the limiting sol...

Semiclassical limit of the derivative nonlinear Schrodinger equation

We study the semiclassical limit of the general derivative nonlinear Schrodinger equation for initial data with Sobolev regularity, before shocks appear in the limit system. The strict hyperbolicity and genuine nonlinearity is proved for the dispersion limit of the derivative nonlinear Schrodinger equation.

Exponential Stability of Nonmonotone Traveling Waves for Nicholson's Blowflies Equation

This paper is concerned with Nicholsons blowflies equation, a kind of time-delayed reaction-diffusion equation. It is known that when the ratio of birth rate coefficient and death rate coefficient satisfies

Shock waves, chiral solitons and semiclassical limit of one-dimensional anyons

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An Asymptotic Limit of a Navier–Stokes System with Capillary Effects

, the equation losses its monotonicity, and its traveling waves are oscillatory when the time-delay

The behaviour of solutions of NLS equation of derivative type in the semiclassical limit

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HOMOGENIZATION OF THE DIRAC-LIKE SYSTEM

or the wave speed

GUIDING CENTER DRIFT INDUCED BY HOMOGENIZATION

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