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Global solution for quantum Zakharov equations

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Abstract

The initial value problem for the quantum Zakharov equation in three dimensions is studied. The existence and uniqueness of a global smooth solution are proven with coupled a priori estimates and the Galerkin method.

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References

  1. Zakharov, V. E. Collapse of Langmuir waves. Journal of Experimental and Theoretical Physics, 35, 908–914 (1972)

    Google Scholar 

  2. Garcia, L. G., Haas, F., de Oliveira, L. P. L., and Goedert, J. Modified Zakharov equations for plasmas with a quantum correction. Physics of Plasmas, 12, 151–155 (2005)

    Google Scholar 

  3. Guo, Y. F., Zhang, J. J., and Guo, B. L. Global well-posedness and the classical limit of the solution for the quantum Zakharov system. Zeitschrift für Angewandte Mathematik und Physik, 64, 53–68 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  4. Fang, S. M., Jin, L. Y., and Guo, B. L. Existence of weak solution for quantum Zakharov equations for plasmas model. Applied Mathematics and Mechanics (English Edition), 32(10), 1339–1344 (2011) DOI 10.1007/s10483-011-1504-7

    Article  MathSciNet  MATH  Google Scholar 

  5. Guo, Y. F., Guo, B. L., and Li, D. L. Asymptotic behaviors of solutions for dissipative quantum Zakharov equations. Applied Mathematics and Mechanics (English Edition), 33(4), 511–524 (2012) DOI 10.1007/s10483-012-1567-8

    Article  MathSciNet  MATH  Google Scholar 

  6. You, S. J., Guo, B. L., and Ning, X. Q. Equations of Langmuir turbulence and Zakharov equations: smoothness and approximation. Applied Mathematics and Mechanics (English Edition), 33(8), 1079–1092 (2012) DOI 10.1007/s10483-012-1606-9

    Article  MathSciNet  MATH  Google Scholar 

  7. Haas, F. and Shukla, P. K. Quantum and classical dynamics of Langmuir wave packets. Physical Review E, 79, 066402 (2009)

    Article  Google Scholar 

  8. Simpson, G., Sulem, C., and Sulem, P. L. Arrest of Langmuir wave collapse by quantum effects. Physical Review E, 80, 056405 (2009)

    Article  Google Scholar 

  9. You, S. J. Existence of global generalized solutions for quantum Zakharov equation in dimension three. Journal of Interdisciplinary Mathematics, 18, 269–281 (2015)

    Article  Google Scholar 

  10. Friedman, A. Partial differential equations. Partial Differential Equations, 24, 44–52 (1969)

    Google Scholar 

  11. Guo, B. L. and Shen, L. J. The existenc and uniqueness of the classical solution and the periodic initial value problem for Zakharov equation. Journal of Labor Research, 3, 310–324 (1982)

    MATH  Google Scholar 

  12. Zhou, Y. L. and Guo, B. L. The periodic boundary value problem and the initial value problem for the generalized Korteweg-de Vries system of higher order. Acta Math. Sinica, 27, 154–176 (1984)

    MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Huaihua University, Huaihua, 418008, Hunan Province, China

    Shujun You

  2. Institute of Applied Physics and Computational Mathematics, Beijing, 100088, China

    Boling Guo

Authors
  1. Shujun You
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  2. Boling Guo
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Corresponding author

Correspondence to Shujun You.

Additional information

Project supported by the National Natural Science Foundation of China (No. 11501232) and the Research Foundation of Education Bureau of Hunan Province (No. 15B185)

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You, S., Guo, B. Global solution for quantum Zakharov equations. Appl. Math. Mech.-Engl. Ed. 38, 603–616 (2017). https://doi.org/10.1007/s10483-017-2181-6

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  • DOI: https://doi.org/10.1007/s10483-017-2181-6

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