Formation of singularities of solutions to the three-dimensional Euler-Boltzmann equations in radiation hydrodynamics

被引：24

作者：

Jiang, Peng ^{[1
,2
]}

Wang, Dehua ^{[2
]}

机构：

[1] Shanghai Jiao Tong Univ, Dept Med, Shanghai 200240, Peoples R China

[2] Univ Pittsburgh, Dept Math, Pittsburgh, PA 15260 USA

来源：

NONLINEARITY | 2010年 / 23卷 / 04期

基金：

美国国家科学基金会;

关键词：

PARTIAL-DIFFERENTIAL-EQUATIONS; COMPRESSIBLE FLUIDS; WAVE-EQUATIONS; DIMENSIONS;

D O I：

10.1088/0951-7715/23/4/003

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The Cauchy problem for the three-dimensional Euler-Boltzmann equations of a polytropic, ideal and isentropic fluid in radiation hydrodynamics is considered. The formation of singularities in smooth solutions is studied. It is proved that some C(1) solutions, regardless of the size of the initial disturbance, will develop singularities in a finite time provided that the initial disturbance satisfies certain conditions.

引用

页码：809 / 821

页数：13

共 50 条

[21] Singularities in three-dimensional compressible Euler flows with vorticity
Stuart, JT
THEORETICAL AND COMPUTATIONAL FLUID DYNAMICS, 1998, 10 (1-4) : 385 - 391
[22] Singularities in Three-Dimensional Compressible Euler Flows with Vorticity
J.T. Stuart
Theoretical and Computational Fluid Dynamics, 1998, 10 : 385 - 391
[23] Formation of singularities of solutions to the compressible Euler equations for a Chaplygin gas
Lai, Geng
Zhu, Mi
APPLIED MATHEMATICS LETTERS, 2022, 129
[24] SINGULARITIES IN SOLUTIONS OF THE THREE-DIMENSIONAL LAMINAR-BOUNDARY-LAYER EQUATIONS.
Williams, James C.
1600, (160):
[25] Manufactured solutions for the three-dimensional Euler equations with relevance to Inertial Confinement Fusion
Waltz, J.
Canfield, T. R.
Morgan, N. R.
Risinger, L. D.
Wohlbier, J. G.
JOURNAL OF COMPUTATIONAL PHYSICS, 2014, 267 : 196 - 209
[26] Global existence of weak solutions to the three-dimensional Euler equations with helical symmetry
Jiu, Quansen
Li, Jun
Niu, Dongjuan
JOURNAL OF DIFFERENTIAL EQUATIONS, 2017, 262 (10) : 5179 - 5205
[27] HERACLES:: a three-dimensional radiation hydrodynamics code
Gonzalez, M.
Audit, E.
Huynh, P.
ASTRONOMY & ASTROPHYSICS, 2007, 464 (02) : 429 - U26
[28] FORMATION OF SINGULARITIES AND EXISTENCE OF GLOBAL CONTINUOUS SOLUTIONS FOR THE COMPRESSIBLE EULER EQUATIONS*
Chen, Geng
Chen, Gui-Qiang G.
Zhu, Shengguo
SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2021, 53 (06) : 6280 - 6325
[29] Local existence and singularities formation for isothermal relativistic radiation hydrodynamics equations
Geng, Yongcai
JOURNAL OF HYPERBOLIC DIFFERENTIAL EQUATIONS, 2016, 13 (04) : 661 - 683
[30] Formation of singularities for the relativistic Euler equations
Athanasiou, Nikolaos
Zhu, Shengguo
JOURNAL OF DIFFERENTIAL EQUATIONS, 2021, 284 : 284 - 317

← 1 2 3 4 5 →