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Large time behavior of solutions for critical and subcritical complex Ginzburg-Landau equations in H1

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Abstract

Considering the Cauchy problem for the critical complex Ginzburg-Landau equation in H1(Rn), we shall show the asymptotic behavior for its solutions in C(0, ∖;H1(Rn)) ∩ L2(0, ∖;H1,2n/(n-2)(R2)), n≥3. Analogous results also hold in the case that the nonlinearity has the subcritical power in H1(Rn), n≥1.

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References

  1. Ginibre, J., Velo, G., The Cauchy problem in local spaces for the complex Ginzburg-Landau equation, I. Compactness method, Physica D, 1996, 95(1): 191–228.

    Article  MATH  MathSciNet  Google Scholar 

  2. Ginibre, J., Velo, G., The Cauchy problem in local spaces for the complex Ginzburg-Landau equation, II. Contraction method, Commun. Math. Phys., 1997, 187(1): 45–79.

    Article  MATH  MathSciNet  Google Scholar 

  3. Wang, B. X., The limit behavior of solutions for the complex Ginzburg-Landau equation, Communications on Pure and Applied Mathematics, 2002, 55(4): 481–508.

    Article  MATH  MathSciNet  Google Scholar 

  4. Keel, M., Tao, T., Endpoint Strichartz estimates, Amer. J. of Math., 1998, 120(6): 955–980.

    Article  MATH  MathSciNet  Google Scholar 

  5. Bergh, J., Löfström, J., Interpolation Spaces, New York: Springer-Verlag, 1976.

    MATH  Google Scholar 

  6. Ginibre, J., Velo, G., On a class of nonlinear Schrödinger equations, J. of Funct. Anal., 1979, 32(1): 1–72.

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Peking University, 100871, Beijing, China

    Baoxiang Wang

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  1. Baoxiang Wang
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Correspondence to Baoxiang Wang.

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Dedicated to Professor Zhou Yulin for his 80th birthday.

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Wang, B. Large time behavior of solutions for critical and subcritical complex Ginzburg-Landau equations in H1 . Sci. China Ser. A-Math. 46, 64–74 (2003). https://doi.org/10.1360/03ys9007

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  • DOI: https://doi.org/10.1360/03ys9007

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