Boltzmann equation and hydrodynamic fluctuations
نویسندگان
چکیده
منابع مشابه
Hydrodynamic Limit of the Stationary Boltzmann Equation in a Slab
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 t...
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The hydrodynamic limit for the Boltzmann equation is studied in the case when the limit system, that is, the system of Euler equations contains contact discontinuities. When suitable initial data is chosen to avoid the initial layer, we prove that there exists a unique solution to the Boltzmann equation globally in time for any given Knudsen number. And this family of solutions converge to the ...
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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 کاملOn 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 کاملBoundary Layers and Hydrodynamic Limits of Boltzmann Equation (i): Incompressible Navier-stokes-fourier Limit
We establish an incompressible Navier-Stokes-Fourier limit for solutions to the Boltzmann equation (with a general collision kernel) considered over a bounded domain. Appropriately scaled families of DiPerna-Lions renormalized solutions with Maxwell reflection boundary conditions are shown to have fluctuations that converge as the Knudsen number ε goes to zero. Every limit point is a weak solut...
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ژورنال
عنوان ژورنال: Physical Review E
سال: 2009
ISSN: 1539-3755,1550-2376
DOI: 10.1103/physreve.80.051202