Local Hilbert Expansion for the Boltzmann Equation
نویسندگان
چکیده
We revisit the classical work of Caflisch [C] for compressible Euler limit of the Boltzmann equation. By using a new L2-L∞ method, we prove the validity of the Hilbert expansion before shock formathions in the Euler system with moderate temperature variation.
منابع مشابه
Hilbert Expansion from the Boltzmann Equation to Relativistic Fluids
We study the local-in-time hydrodynamic limit of the relativistic Boltzmann equation using a Hilbert expansion. More specifically, we prove the existence of local solutions to the relativistic Boltzmann equation that are nearby the local relativistic Maxwellian constructed from a class of solutions to the relativistic Euler equations that includes a large subclass of near-constant, non-vacuum f...
متن کاملFractional diffusion limit for collisional kinetic equations: a Hilbert expansion approach
We develop a Hilbert expansion approach for the derivation of fractional diffusion equations from the linear Boltzmann equation with heavy tail equilibria. 1 Setting of the result 1.
متن کاملExternal and Internal Incompressible Viscous Flows Computation using Taylor Series Expansion and Least Square based Lattice Boltzmann Method
The lattice Boltzmann method (LBM) has recently become an alternative and promising computational fluid dynamics approach for simulating complex fluid flows. Despite its enormous success in many practical applications, the standard LBM is restricted to the lattice uniformity in the physical space. This is the main drawback of the standard LBM for flow problems with complex geometry. Several app...
متن کاملAn algebraic calculation method for describing time-dependent processes in electrochemistry – Expansion of existing procedures
In this paper an alternative model allowing the extension of the Debye-Hückel Theory (DHT) considering time dependence explicitly is presented. From the Electro-Quasistatic approach (EQS) introduced in earlier studies time dependent potentials are suitable to describe several phenomena especially conducting media as well as the behaviour of charged particles (ions) in electrolytes. This leads t...
متن کاملSharp Interface Motion of a Binary Fluid Mixture
We derive hydrodynamic equations describing the evolution of a binary fluid segregated into two regions, each rich in one species, which are separated (on the macroscopic scale) by a sharp interface. Our starting point is a Vlasov-Boltzmann (VB) equation describing the evolution of the one particle position and velocity distributions, fi(x, v, t), i = 1, 2. The solution of the VB equation is de...
متن کامل