Hydrodynamic Limit of the Stationary Boltzmann Equation in a Slab
نویسندگان
چکیده
We study the stationary solution of the Boltzmann equation in a slab with a constant external force parallel to the boundary and complete accommodation condition on the walls at a specified temperature. We prpve that when the force is sufficiently small there exists a solution which converges, in the hydrodynamic limit, to a local Maxwellian with parameters given by the stationary solution of the corresponding compressible Navier-Stokes equations with no-slip boundary conditions. Corrections to this Maxwellian are obtained in powers of the Knudsen number with a controlled remainder.
منابع مشابه
On the Milne Problem and the Hydrodynamic Limit for a Steady Boltzmann Equation Model
For a stationary nonlinear Boltzmann equation in a slab with a particular truncation in the collision operator, the Milne problem for the boundary layer together with a weak type of hydrodynamic behaviour in the interior of the slab, are studied by non-perturbative methods in the small mean free path limit.
متن کاملHydrodynamic Limit with Geometric Correction of Stationary Boltzmann Equation
We consider the hydrodynamic limit of a stationary Boltzmann equation in a unit plate with in-flow boundary. The classical theory claims that the solution can be approximated by the sum of interior solution which satisfies steady incompressible Navier-Stokes-Fourier system, and boundary layer derived from Milne problem. In this paper, we construct counterexamples to disprove such formulation in...
متن کاملThe Stationary Boltzmann Equation in the Slab with given Weighted Mass for Hard and Soft Forces
The stationary Boltzmann equation for hard and soft forces is considered in the slab. An L 1 existence theorem is proven in a given indata context with xed total weighted mass. In the proof a new direct approach is introduced, which uses a certain coupling between mass and boundary ow. Compactness properties are extracted from entropy production estimates and from the boundary behaviour.
متن کاملThe Stationary Boltzmann equation for a two component gas in the slab with different molecular masses
The stationary Boltzmann equation for hard and soft forces in the context of a two component gas is considered in the slab when the molecular masses of the 2 component are different. An L existence theorem is proved when one component satisfies a given indata profile and the other component satisfies diffuse reflection at the boundaries. Weak L compactness is extracted from the control of the e...
متن کاملStability of the Laminar Solution of the Boltzmann Equation for the Benard Problem
We consider the Boltzmann equation for a gas in a horizontal slab, subject to a gravitational force. The boundary conditions are of diffusive type, specifying the wall temperatures, so that the top temperature is lower than the bottom one (Benard setup). We consider a 1-dimensional stationary solution, which is close for small Knudsen number to the laminar purely conductive stationary solution ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1994