2017/03/23 by Renjun Duan, Yong Wang, Duan, Renjun +1 · 1 citation
Computer Science · Mathematics · #35B45 #76P05 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Gas Dynamics and Kinetic Theory #Navier-Stokes equation solutions #Primary 35Q20 #Secondary 35A01
paper · pdf · doi:10.48550/arxiv.1703.07978
openalex publication_date 2017/03/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The paper is devoted to constructing the global solutions around global Maxwellians to the initial-boundary value problem on the Boltzmann equation in general bounded domains with isothermal diffuse reflection boundaries. We allow a class of non-negative initial data which have arbitrary large amplitude and even contain vacuum. The result shows that the oscillation of solutions away from global Maxwellians becomes small after some positive time provided that they are initially close to each other in L2. This yields the disappearance of any initial vacuum and the exponential convergence of large-amplitude solutions to equilibrium in large time. The isothermal diffuse reflection boundary condition plays a vital role in the analysis. The most key ingredients in our strategy of the proof include: (i) L2x,v--L^∞xL1v--L^∞x,v estimates along a bootstrap argument; (ii) Pointwise estimates on the upper bound of the gain term by the product of L^∞ norm and L2 norm; (iii) An iterative procedure on the nonlinear term.