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On growth in time of Sobolev norms of smooth solutions of nonlinear Schrödinger equations in ℝD

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References

  1. J. Bourgain,Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations, I: Schrödinger equations, Geom. Funct. Anal.3 (1993), 107–156.

    Article  MATH  MathSciNet  Google Scholar 

  2. J. Bourgain,On the growth in time of higher Sobolev norms of smooth solutions of Hamiltonian PDE, Internat. Math. Res. Notices (1996), 277–304.

  3. G. Staffilani,Quadratic forms for a 2D semilinear Schrödinger equation. Duke Math. J.86 (1997), 79–108.

    Article  MATH  MathSciNet  Google Scholar 

  4. G. Staffilani,On the growth of high Sobolov norms of solutions for KdV and Schrödinger equations, Duke Math. J.86 (1997), 109–142.

    Article  MATH  MathSciNet  Google Scholar 

  5. J. Lin and W. Strauss,Decay and scattering of solutions of a nonlinear Schrödinger equation, J. Funct. Anal.30 (1978), 245–263.

    Article  MATH  MathSciNet  Google Scholar 

  6. C. Kenig, G. Ponce and L. Vega,On the IVP for the nonlinear Schrödinger equation, inHarmonic Analysis and Operator Theory, Contemp. Math. (1995), 353–368.

  7. Y. Tsutsumi and K. Yajima,The asymptotic behaviour of nonlinear Schrödinger equations, Bull. Amer. Math. Soc.11 (1984), 176–188.

    Article  MathSciNet  Google Scholar 

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Bourgain, J. On growth in time of Sobolev norms of smooth solutions of nonlinear Schrödinger equations in ℝD . J. Anal. Math. 72, 299–310 (1997). https://doi.org/10.1007/BF02843163

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