Formation of singularities of solutions to a 1D compressible radiation hydrodynamics model. (September 2022)

• Record Type: Journal Article
• Authors: Li, Shengxin; Wang, Jing
• Is Part Of: Nonlinear analysis. Volume 222(2022)
• Publication Date: 2022-09
• Subjects: Compressible radiation hydrodynamics -- Formation of singularities -- Characteristic curve methods -- Riemann invariants -- Shock singularity; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2022.112969
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper we are concerned with a 1D compressible radiation hydrodynamics model, which is described by a Navier–Stokes-elliptic coupled system of equations without viscosity. We prove that the smooth solutions to this model would blow up in finite time provided the first derivatives of the initial data are less than some negative constant although the initial data themselves are small. Moreover, it is shown that the singularity is indeed a shock singularity.