TY - JOUR
T1 - Incompressible hydrodynamic approximation with viscous heating to the Boltzmann equation
AU - Guo, Yan
AU - Liu, Shuangqian
N1 - Publication details (e.g. title, author(s), publication statuses and dates) are captured on an “AS IS” and “AS AVAILABLE” basis at the time of record harvesting from the data source. Suggestions for further amendments or supplementary information can be sent to lbscholars@cityu.edu.hk.
PY - 2017/11/1
Y1 - 2017/11/1
N2 - 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.
AB - 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.
KW - Incompressible Navier-Stokes-Fourier system
KW - L 2-L ∞ approach
KW - super-Burnett functions
KW - viscous heating
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U2 - 10.1142/S0218202517500440
DO - 10.1142/S0218202517500440
M3 - RGC 21 - Publication in refereed journal
VL - 27
SP - 2261
EP - 2296
JO - Mathematical Models and Methods in Applied Sciences
JF - Mathematical Models and Methods in Applied Sciences
SN - 0218-2025
IS - 12
ER -