2013/09/28 by Yachun Li, Li, Yachun, Shengguo Zhu +1
Mathematics · Physics and Astronomy · #35A05 #35B40 #35L65 #76Y05 #85A05 #Advanced Mathematical Physics Problems #FOS: Physical sciences #Gas Dynamics and Kinetic Theory #Mathematical Physics (math-ph) #Navier-Stokes equation solutions #Secondary: 35B35 #math-ph #math.MP #msc:35A05 #msc:35B35 #msc:35B40 #msc:35L65 #msc:76Y05 #msc:85A05
paper · pdf · doi:10.48550/arxiv.1309.7420
28 pages
openalex publication_date 2013/09/28 · arxiv created 2014/10/07 · arxiv updated 2014/10/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we discuss the Cauchy Problem for the compressible isentropic Euler-Boltzmann equations with vacuum in radiation hydrodynamics. Firstly, we establish the local existence of regular solutions by the fundamental methods in the theory of quasi-linear symmetric hyperbolic systems under some physical assumptions. Then we give the non-global existence of regular solutions caused by the effect of vacuum for 1<γ≤ 3. Finally, we extend our result to the initial-boundary value problem under some suitable boundary conditions. These blow-up results tell us that the radiation cannot prevent the formation of singularities caused by the appearance of vacuum.