The Lifespan of Spherically Symmetric Solutions of the Compressible Euler Equations Outside an Impermeable Sphere
Annales de l'I.H.P. Analyse non linéaire, Tome 26 (2009) no. 6, pp. 2227-2252. 
@article{AIHPC_2009__26_6_2227_0,
     author = {Godin, Paul},
     title = {The {Lifespan} of {Spherically} {Symmetric} {Solutions} of the {Compressible} {Euler} {Equations} {Outside} an {Impermeable} {Sphere}},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {2227--2252},
     publisher = {Elsevier},
     volume = {26},
     number = {6},
     year = {2009},
     doi = {10.1016/j.anihpc.2009.03.002},
     mrnumber = {2569893},
     zbl = {1178.35298},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.anihpc.2009.03.002/}
}
TY  - JOUR
AU  - Godin, Paul
TI  - The Lifespan of Spherically Symmetric Solutions of the Compressible Euler Equations Outside an Impermeable Sphere
JO  - Annales de l'I.H.P. Analyse non linéaire
PY  - 2009
SP  - 2227
EP  - 2252
VL  - 26
IS  - 6
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.anihpc.2009.03.002/
DO  - 10.1016/j.anihpc.2009.03.002
LA  - en
ID  - AIHPC_2009__26_6_2227_0
ER  - 
%0 Journal Article
%A Godin, Paul
%T The Lifespan of Spherically Symmetric Solutions of the Compressible Euler Equations Outside an Impermeable Sphere
%J Annales de l'I.H.P. Analyse non linéaire
%D 2009
%P 2227-2252
%V 26
%N 6
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.anihpc.2009.03.002/
%R 10.1016/j.anihpc.2009.03.002
%G en
%F AIHPC_2009__26_6_2227_0
Godin, Paul. The Lifespan of Spherically Symmetric Solutions of the Compressible Euler Equations Outside an Impermeable Sphere. Annales de l'I.H.P. Analyse non linéaire, Tome 26 (2009) no. 6, pp. 2227-2252. doi : 10.1016/j.anihpc.2009.03.002. http://www.numdam.org/articles/10.1016/j.anihpc.2009.03.002/

[1] Alinhac S., Temps De Vie Des Solutions Régulières Des Équations D'Euler Compressibles Axisymétriques En Dimension 2, Invent. Math. 111 (1993) 627-670. | MR | Zbl

[2] Godin P., Long Time Behaviour of Solutions to Some Nonlinear Rotation Invariant Mixed Problems, Comm. Partial Differential Equations 14 (3) (1989) 299-374. | MR | Zbl

[3] Godin P., The Lifespan of a Class of Smooth Spherically Symmetric Solutions of the Compressible Euler Equations With Variable Entropy in Three Space Dimensions, Arch. Ration. Mech. Anal. 177 (2005) 479-511. | MR | Zbl

[4] Godin P., The Lifespan of Solutions of Exterior Radial Quasilinear Cauchy-Neumann Problems, J. Hyperbolic Differ. Equ. 5 (3) (2008) 519-546. | MR | Zbl

[5] Guès O., Problème Mixte Hyperbolique Quasi-Linéaire Caractéristique, Comm. Partial Differential Equations 15 (5) (1990) 595-645. | MR | Zbl

[6] Hörmander L., The Analysis of Linear Partial Differential Operators I, Grundlehren Math. Wiss., vol. 256, Springer, Berlin, 1983. | MR | Zbl

[7] Hörmander L., The Lifespan of Classical Solutions of Non-Linear Hyperbolic Equations, in: Cordes H. O., Gramsch B., Widom H. (Eds.), Pseudo-Differential Operators, Lecture Notes in Math., vol. 1256, Springer, Berlin, 1987, pp. 214-280. | MR | Zbl

[8] John F., Blow-Up of Radial Solutions of u tt =c 2 u t Δu in Three Space Dimensions, Mat. Apl. Comput. 4 (1) (1985) 3-18. | MR | Zbl

[9] Klainerman S., Sideris T., On Almost Global Existence for Nonrelativistic Wave Equations in 3D, Comm. Pure Appl. Math. 49 (1996) 307-322. | MR | Zbl

[10] Schochet S., The Compressible Euler Equations in a Bounded Domain: Existence of Solutions and the Incompressible Limit, Comm. Math. Phys. 104 (1986) 49-75. | MR | Zbl

[11] Secchi P., Well-Posedness of Characteristic Symmetric Hyperbolic Systems, Arch. Ration. Mech. Anal. 134 (1996) 155-197. | MR | Zbl

[12] Sideris T., Delayed Singularity Formation in 2D Compressible Flow, Amer. J. Math. 119 (1997) 371-422. | MR | Zbl

Cité par Sources :