Global well-posedness for a $L^2$-critical nonlinear higher-order Schrödinger equation

@article{Dinh2017GlobalWF,
  title={Global well-posedness for a \$L^2\$-critical nonlinear higher-order Schr{\"o}dinger equation},
  author={Van Duong Dinh},
  journal={Journal of Mathematical Analysis and Applications},
  year={2017},
  volume={458},
  pages={174-192}
}
  • Van Duong Dinh
  • Published 2 March 2017
  • Mathematics
  • Journal of Mathematical Analysis and Applications
View PDF on arXiv
1 Citations

One Citation

Global existence for the defocusing mass-critical nonlinear fourth-order Schrödinger equation below the energy space

In this paper, we consider the defocusing mass-critical nonlinear fourth-order Schrodinger equation. Using the $I$-method combined with the interaction Morawetz estimate, we prove that the problem is…

References

SHOWING 1-10 OF 25 REFERENCES

Global well-posedness and scattering for the defocusing, $L^{2}$-critical, nonlinear Schrödinger equation when $d=2$

In this paper we prove that the defocusing, quintic nonlinear Schr\"odinger initial value problem is globally well-posed and scattering for $u_{0} \in L^{2}(\mathbf{R})$. To do this, we will prove a…

Well-posedness of nolinear fractional Schr\"odinger and wave equations in Sobolev spaces

We prove the well-posed results in sub-critical and critical cases for the pure power-type nonlinear fractional Schr\"odinger equations on $\mathbb{R}^d$. These results extend the previous ones in…

Improved almost Morawetz estimates for the cubic nonlinear Schrodinger equation

We prove global well-posedness for the cubic, defocusing, nonlinear Schr{\"o}dinger equation on $\mathbf{R}^{2}$ with data $u_{0} \in H^{s}(\mathbf{R}^{2})$, $s > 1/4$. We accomplish this by…

Resonant decompositions and the $I$-method for the cubic nonlinear Schrödinger equation on $\mathbb{R}^2$

The initial value problem for the cubic defocusing nonlinear Schrodinger equation $i \partial_t u + \Delta u = |u|^2 u$ on theplane is shown to be globally well-posed for initial data in $H^s…

Improved interaction Morawetz inequalities for the cubic nonlinear Schr

We prove global well-posedness for low regularity data for the $L^2-critical$ defocusing nonlinear Schr\"odinger equation (NLS) in 2d. More precisely we show that a global solution exists for…

Well-posedness of Cauchy problem for the fourth order nonlinear Schrödinger equations in multi-dimensional spaces

Bootstrapped Morawetz Estimates And Resonant Decomposition For Low Regularity Global Solutions Of Cubic NLS On R^{2}

We prove global well-posedness for the L^{2}-critical cubic defocusing nonlinear Schr\"odinger equation on R^{2} with data u_{0} \in H^{s}(R^{2}) for s > {1/3}.

Global existence of solutions for a fourth-order nonlinear Schrödinger equation in n+1 dimensions

On well-posedness, regularity and ill-posedness for the nonlinear fourth-order Schrödinger equation

  • Van Duong Dinh
  • Mathematics
    Bulletin of the Belgian Mathematical Society - Simon Stevin
  • 2018
We prove the local well-posedness for the nonlinear fourth-order Schrodinger equation (NL4S) in Sobolev spaces. We also study the regularity of solutions in the sub-critical case. A direct…

Well-posedness for the fourth-order Schrödinger equations with quadratic nonlinearity

This paper is concerned with 1-D quadratic semilinear fourth-order Schrödinger equations. Motivated by the quadratic Schrödinger equations in the pioneer work of Kenig-Ponce-Vega [12], three…