# 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
1 Citations
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

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
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
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
• Mathematics
• 2008
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 $H^s • Mathematics • 2007 We prove global well-posedness for low regularity data for the$L^2-critical\$ defocusing nonlinear Schr\"odinger equation (NLS) in 2d. More precisely we show that a global solution exists for
• Mathematics
• 2008
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}.
• 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
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