American Institute of Mathematical Sciences

Advanced
2011, 2011(Special): 1448-1456. doi: 10.3934/proc.2011.2011.1448

Cylindrical blowup solutions to the isothermal Euler-Poisson equations

Manwai Yuen 1,

1. 

Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, China

Received  June 2010 Revised  February 2011 Published  October 2011

This proceeding is the continued version of the analytical blowup solutions for 2-dimensional Euler-Poisson equations in ”M.W. Yuen, Analytical Blowup Solutions to the 2-dimensional Isothermal Euler-Poisson Equations of Gaseous Stars, J. Math. Anal. Appl. 341 (2008), 445–456”. With the extension of the blowup solutions with radial symmetry for the isothermal Euler-Poisson equations in R$^2$, the cylindrical blowup solutions in R$^N$ ($N>=3$) with are constructed by the separation method. Here, the constructed 3-dimensional blowup solutions could be applied to interpret the evolution of cylindrical cloud for star formation in astrophysics.
Keywords: $R^N$, global solutions, classical solutions, Euler-Poisson equations, blowup, star formation, isothermal, cylindrical, Analytical solutions.
Mathematics Subject Classification: Primary: 35Q85 85A15; Secondary: 35B44, 35Q30, 35Q35, 85A05.
Citation: Manwai Yuen. Cylindrical blowup solutions to the isothermal Euler-Poisson equations. Conference Publications, 2011, 2011 (Special) : 1448-1456. doi: 10.3934/proc.2011.2011.1448
[1]

Hong Cai, Zhong Tan. Stability of stationary solutions to the compressible bipolar Euler-Poisson equations. Discrete and Continuous Dynamical Systems, 2017, 37 (9) : 4677-4696. doi: 10.3934/dcds.2017201
[2]

La-Su Mai, Kaijun Zhang. Asymptotic stability of steady state solutions for the relativistic Euler-Poisson equations. Discrete and Continuous Dynamical Systems, 2016, 36 (2) : 981-1004. doi: 10.3934/dcds.2016.36.981
[3]

Yongcai Geng. Singularity formation for relativistic Euler and Euler-Poisson equations with repulsive force. Communications on Pure and Applied Analysis, 2015, 14 (2) : 549-564. doi: 10.3934/cpaa.2015.14.549
[4]

Myoungjean Bae, Yong Park. Radial transonic shock solutions of Euler-Poisson system in convergent nozzles. Discrete and Continuous Dynamical Systems - S, 2018, 11 (5) : 773-791. doi: 10.3934/dcdss.2018049
[5]

Masahiro Suzuki. Asymptotic stability of stationary solutions to the Euler-Poisson equations arising in plasma physics. Kinetic and Related Models, 2011, 4 (2) : 569-588. doi: 10.3934/krm.2011.4.569
[6]

Qiwei Wu, Liping Luan. Large-time behavior of solutions to unipolar Euler-Poisson equations with time-dependent damping. Communications on Pure and Applied Analysis, 2021, 20 (3) : 995-1023. doi: 10.3934/cpaa.2021003
[7]

Zhigang Wu, Weike Wang. Pointwise estimates of solutions for the Euler-Poisson equations with damping in multi-dimensions. Discrete and Continuous Dynamical Systems, 2010, 26 (3) : 1101-1117. doi: 10.3934/dcds.2010.26.1101
[8]

Tianhong Li. Some special solutions of the multidimensional Euler equations in $R^N$. Communications on Pure and Applied Analysis, 2005, 4 (4) : 757-762. doi: 10.3934/cpaa.2005.4.757
[9]

Yeping Li. Existence and some limit analysis of stationary solutions for a multi-dimensional bipolar Euler-Poisson system. Discrete and Continuous Dynamical Systems - B, 2011, 16 (1) : 345-360. doi: 10.3934/dcdsb.2011.16.345
[10]

Qiwei Wu. Large-time behavior of solutions to the bipolar quantum Euler-Poisson system with critical time-dependent over-damping. Discrete and Continuous Dynamical Systems - B, 2022  doi: 10.3934/dcdsb.2022008
[11]

A. Alexandrou Himonas, Gerard Misiołek, Feride Tiǧlay. On unique continuation for the modified Euler-Poisson equations. Discrete and Continuous Dynamical Systems, 2007, 19 (3) : 515-529. doi: 10.3934/dcds.2007.19.515
[12]

Jianwei Yang, Dongling Li, Xiao Yang. On the quasineutral limit for the compressible Euler-Poisson equations. Discrete and Continuous Dynamical Systems - B, 2022  doi: 10.3934/dcdsb.2022020
[13]

Thierry Cazenave, Flávio Dickstein, Fred B. Weissler. Multi-scale multi-profile global solutions of parabolic equations in $\mathbb{R}^N $. Discrete and Continuous Dynamical Systems - S, 2012, 5 (3) : 449-472. doi: 10.3934/dcdss.2012.5.449
[14]

Yulan Xu, Yanping Dou. Large BV solutions to Euler equations in the isothermal self-gravitating gases with damping. Communications on Pure and Applied Analysis, 2009, 8 (4) : 1451-1467. doi: 10.3934/cpaa.2009.8.1451
[15]

Jerry L. Bona, Stéphane Vento, Fred B. Weissler. Singularity formation and blowup of complex-valued solutions of the modified KdV equation. Discrete and Continuous Dynamical Systems, 2013, 33 (11&12) : 4811-4840. doi: 10.3934/dcds.2013.33.4811
[16]

Peixin Zhang, Jianwen Zhang, Junning Zhao. On the global existence of classical solutions for compressible Navier-Stokes equations with vacuum. Discrete and Continuous Dynamical Systems, 2016, 36 (2) : 1085-1103. doi: 10.3934/dcds.2016.36.1085
[17]

José A. Carrillo, Renjun Duan, Ayman Moussa. Global classical solutions close to equilibrium to the Vlasov-Fokker-Planck-Euler system. Kinetic and Related Models, 2011, 4 (1) : 227-258. doi: 10.3934/krm.2011.4.227
[18]

Xiang-Dong Fang. Positive solutions for quasilinear Schrödinger equations in $\mathbb{R}^N$. Communications on Pure and Applied Analysis, 2017, 16 (5) : 1603-1615. doi: 10.3934/cpaa.2017077
[19]

E. N. Dancer, Shusen Yan. On the existence of multipeak solutions for nonlinear field equations on $R^N$. Discrete and Continuous Dynamical Systems, 2000, 6 (1) : 39-50. doi: 10.3934/dcds.2000.6.39
[20]

Kazuhiro Ishige, Tatsuki Kawakami. Asymptotic behavior of solutions for some semilinear heat equations in $R^N$. Communications on Pure and Applied Analysis, 2009, 8 (4) : 1351-1371. doi: 10.3934/cpaa.2009.8.1351

 Impact Factor: 

Tools

Metrics

  • PDF downloads (58)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2022 American Institute of Mathematical Sciences | Privacy Policy