Incompressible hydrodynamic approximation with viscous heating to the Boltzmann equation

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Original languageEnglish
Pages (from-to)2261-2296
Journal / PublicationMathematical Models and Methods in Applied Sciences
Issue number12
Publication statusPublished - 1 Nov 2017
Externally publishedYes


The incompressible Navier-Stokes-Fourier (INSF) system with viscous heating was first derived from the Boltzmann equation in the form of the diffusive scaling by Bardos-Levermore-Ukai-Yang [Kinetic equations: Fluid dynamical limits and viscous heating, Bull. Inst. Math. Acad. Sin.(N.S.) 3 (2008) 1-49]. The purpose of this paper is to justify such an incompressible hydrodynamic approximation to the Boltzmann equation in L2 a L∞ setting in a periodic box. Based on an odd-even expansion of the solution with respect to the microscopic velocity, the diffusive coefficients are determined by the INSF system with viscous heating and the super-Burnett functions. More importantly, the remainder of the expansion is proven to decay exponentially in time via an L2-L∞ approach on the condition that the initial data satisfies the mass, momentum and energy conversation laws.

Research Area(s)

  • Incompressible Navier-Stokes-Fourier system, L 2-L ∞ approach, super-Burnett functions, viscous heating

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