2013/09/28 by Yachun Li, Li, Yachun, Shengguo Zhu +1
Engineering · Mathematics · Physics and Astronomy · #35A09 #35B44 #35M31 #35Q35 #35Q85 #Advanced Mathematical Physics Problems #Computational Fluid Dynamics and Aerodynamics #FOS: Physical sciences #Mathematical Physics (math-ph) #Navier-Stokes equation solutions #Secondary: 35Q31 #math-ph #math.MP #msc:35A09 #msc:35B44 #msc:35M31 #msc:35Q31 #msc:35Q35 #msc:35Q85
paper · pdf · doi:10.48550/arxiv.1309.7419
31pages
openalex publication_date 2013/09/28 · arxiv created 2014/01/13 · arxiv updated 2014/01/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the Cauchy problem for multi-dimensional compressible radiation hydrodynamics equations with vacuum. First, we present some sufficient conditions on the blow-up of smooth solutions in multi-dimensional space. Then, we obtain the invariance of the support of density for the smooth solutions with compactly supported initial mass density by the property of the system under the vacuum state. Based on the above-mentioned results, we prove that we cannot get a global classical solution, no matter how small the initial data are, as long as the initial mass density is of compact support. Finally, we will see that some of the results that we obtained are still valid for the isentropic flows with degenerate viscosity coefficients as well as 1-D case.