Journal ArticleDOI
A classification of well‐posed kinetic layer problems
TLDR
In this article, the half space boundary value problem for the Boltzmann equation with an incoming distribution was studied and the boundary layer arising in the kinetic theory of gases as the mean free path tends to zero.Abstract:
In the first part of this paper, we study the half space boundary value problem for the Boltzmann equation with an incoming distribution, obtained when considering the boundary layer arising in the kinetic theory of gases as the mean free path tends to zero. We linearize it about a drifting Maxwellian and prove that, as conjectured by Cercignani [4], the problem is well-posed when the drift velocity u exceeds the sound speed c, but that one (respectively four, five) additional conditions must be imposed when 0 < u < c (respectively - c < u < 0 and u < - c). In the second part, we show that the well-posedness and the asymptotic behavior results for kinetic layers equations with prescribed incoming flux can be extended to more general and realistic boundary conditions.read more
Citations
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Journal ArticleDOI
Contact discontinuity with general perturbations for gas motions
TL;DR: In this article, the authors obtained the large time asymptotic stability of a contact wave pattern with a convergence rate for the Navier-Stokes equations and the Boltzmann equation in a uniform way.
Journal ArticleDOI
Numerical analysis of gas flows condensing on its plane condensed phase on the basis of kinetic theory
TL;DR: In this paper, the formation and propagation of disturbances in an initially uniform gas blowing against its plane condensed phase are investigated under the conventional boundary condition on the condensed phase to supplement the authors' previous work, where some solutions require more detailed computation.
Journal ArticleDOI
Nonlinear Stability of Rarefaction Waves for the Boltzmann Equation
TL;DR: In this article, it was shown that rarefaction waves for the Boltzmann equation are time-asymptotic stable and tend to the rare-faction wave for the Euler and Navier-Stokes equations.
Journal ArticleDOI
Model equations in rarefied gas dynamics: Viscous-slip and thermal-slip coefficients
C. E. Siewert,Felix Sharipov +1 more
TL;DR: In this article, various model equations are used to define the viscous-slip and the thermal-slink coefficients in rarefied gas dynamics, and the important issue of how to define meaningful ways (appropriate mean-free paths) to compare the results for the various models is discussed.
Journal ArticleDOI
Nonlinear Boundary Layers of the Boltzmann Equation: I. Existence
TL;DR: In this paper, the half-space problem of the nonlinear Boltzmann equation was studied, and it was shown that the solvability of the problem changes with the Mach number ℳ∞ of the far field.
References
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Journal ArticleDOI
Asymptotic Theory of the Boltzmann Equation
TL;DR: In this article, a generalization of the Hilbert and Enskog expansions is described in terms of extended sets of macroscopic state variables, each governed by partial differential equations similar to those found in fluid dynamics but sufficiently general to approximate an arbitrary distribution function.
Journal ArticleDOI
The milne and kramers problems for the boltzmann equation of a hard sphere gas
TL;DR: In this paper, the existence, uniqueness and properties of asymptotic behavior for solutions of the Milne and Kramers problems for the linearized Boltzmann equation for a gas of hard spheres are proved.