scholarly journals Global $L^{\infty}$ solutions of the compressible Euler equations with spherical symmetry

2006 ◽  
Vol 46 (3) ◽  
pp. 457-524 ◽  
Author(s):  
Naoki Tsuge
Keyword(s):  
Euler Equations ◽  
Spherical Symmetry ◽  
Compressible Euler Equations ◽  
Compressible Euler

scholarly journals Blowup Phenomenon of Solutions for the IBVP of the Compressible Euler Equations in Spherical Symmetry

2016 ◽  
Vol 2016 ◽  
pp. 1-6
Author(s):  
Ka Luen Cheung ◽  
Sen Wong
Keyword(s):  
Positive Integer ◽  
Boundary Value Problem ◽  
Euler Equations ◽  
Spherical Symmetry ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Compressible Euler Equations ◽  
Compressible Euler ◽  
Isothermal Case ◽  
Initial Boundary Value

The blowup phenomenon of solutions is investigated for the initial-boundary value problem (IBVP) of theN-dimensional Euler equations with spherical symmetry. We first show that there are only trivial solutions when the velocity is of the formc(t)xα-1x+b(t)(x/x)for any value ofα≠1or any positive integerN≠1. Then, we show that blowup phenomenon occurs whenα=N=1andc2(0)+c˙(0)<0. As a corollary, the blowup properties of solutions with velocity of the form(a˙t/at)x+b(t)(x/x)are obtained. Our analysis includes both the isentropic case(γ>1)and the isothermal case(γ=1).

scholarly journals Singularity Formation for the Compressible Euler Equations

2017 ◽  
Vol 49 (4) ◽  
pp. 2591-2614 ◽  
Author(s):  
Geng Chen ◽  
Ronghua Pan ◽  
Shengguo Zhu
Keyword(s):  
Euler Equations ◽  
Compressible Euler Equations ◽  
Singularity Formation ◽  
Compressible Euler

Transonic Shock Formation in a Rarefaction Riemann Problem for the 2D Compressible Euler Equations

2008 ◽  
Vol 69 (3) ◽  
pp. 720-742 ◽  
Author(s):  
James Glimm ◽  
Xiaomei Ji ◽  
Jiequan Li ◽  
Xiaolin Li ◽  
Peng Zhang ◽  
...  
Keyword(s):  
Euler Equations ◽  
Riemann Problem ◽  
Compressible Euler Equations ◽  
Shock Formation ◽  
Transonic Shock ◽  
Compressible Euler
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