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Stability and Unstability of the Standing Wave to Euler Equations

  • Xiuli Tang (a1), Xiuqing Wang (a2) and Ganshan Yang (a2)

In this paper, we first discuss the well-posedness of linearizing equations, and then study the stability and unstability of the 3-D compressible Euler Equation, by analysing the existence of saddle point. In addition, we give the existence of local solutions of the compressible Euler equation.

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*Corresponding author. Email: (G. S. Yang)
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[1] Dafermos C., Hyperbolic Conservation Laws in Continuum Physics, Second Edition, Grundlehren der Mathematischen Wissenschaften, Fundamental Principles of Mathematical Sciences, 2005.
[2] Majda A., Compressible Fluid Flow and Systems of Conservation Laws in Several Space Variables, Applied Math. Sciences, New York, 1984.
[3] Sideris T. C., Formation of singularities in three-dimensional compressible fluids, Commun. Math. Phys., 101 (1985), pp. 475485.
[4] Makino T., Blowing up solutiona of the Euler-Poisson equation for the evolution of gaseous stars, Transport Theory Statist. Phys., 21 (1992), pp. 615624.
[5] Friedlander Susan and Vishik Misha M., Lax pair formulation for the Euler equation, Phys. Lett. A., 148 (1990), pp. 313319.
[6] Deng Y., Liu T. P., Yang T., and Yao Z. A., Solutions of EulerCPoisson equations for gaseous stars, Arch. Rational Mech. Anal., 164 (2002), pp. 261285.
[7] Li T. H., Some special solutions of the Euler equation in RN , Commun. Pure Appl. Anal., 4 (2005), pp. 757762.
[8] Guo B. L., Yang G. S. and Pu X. K., Blow-up and global smooth solutions for incompressible three-dimensional Navier-Stokes equations, China Phys. Lett., 25 (2008), pp. 21152117.
[9] Ma W. X. and Chen M., Direct search for exact solutions to the nonlinear Schrödinger equation, Appl. Math. Comput., 215 (2009), pp. 28352842.
[10] Xing , Ma Wenxiu, Yu Jun and Khalique Chaudry Masood, Solitary waves with the Madelung fluid description: A generalized derivative nonlinear Schrödinger equation, Commun. Nonlinear Sci. Numer. Simulation, 31 (2016), pp. 4046.
[11] Xing and Lin Fuhong, Soliton excitations and shape-changing collisions in alphahelical proteins with interspine coupling at higher order, Commun. Nonlinear Sci. Numer. Simulation, 32 (2016), pp. 241261.
[12] Xing,Madelung fluid description on a generalized mixed nonlinear Schrödinger equation, Nonlinear Dynamics, 81 (2015), pp. 239247.
[13] Xing, Ma Wenxiu and Khalique Chaudry Masood, A direct bilinear Bäcklund transformation of a (2+1)-dimensional Korteweg-de Vries-like model, Appl.Math. Lett., 50 (2015), pp. 3742.
[14] Xing , Ma Wenxiu, Yu Jun, Lin Fuhong and Khalique Chaudry Masood, Envelope bright- and dark-soliton solutions for the GerdjikovCIvanov model, Nonlinear Dynamics, 82 (2015), pp. 12111220.
[15] Guo Yan, Jiang Juhi and Jiang Ning, Acoustic limit for the Boltzmann equation in optimal scaling, Commun. Pure Appl. Math., LXIII (2010), pp. 0337–0361.
[16] Song Wenjing, Li Hua, Yang Ganshan, and Yuan George Xianzhi, Nonhomogeneous boundary value problem for (I, J) similar solutions o incompressible two-dimensional Euler equations, J. Inequalities Applications, 2014 (2014), pp. 115.
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Advances in Applied Mathematics and Mechanics
  • ISSN: 2070-0733
  • EISSN: 2075-1354
  • URL: /core/journals/advances-in-applied-mathematics-and-mechanics
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