Low regularity blowup solutions for the mass-critical NLS in higher dimensions

Abstract

In this paper, we study the $H^s$-stability of the log-log blowup regime (which has been completely described in a series of recent works by Merle and Raphael) for the focusing mass-critical nonlinear Schrödinger equations $i{\partial }_{t}u+\Delta u+|u{|}^{\frac{4}{d}}u=0$ in ${\mathbb{R}}^d$ with $d\ge 3$. We aim to extend the result in [Colliander and Raphael, Rough blowup solutions to the $L^2$ critical NLS, Math. Anna., 345(2009), 307-366.] for dimension two to the higher dimensions cases $d\ge 3$, where we use the bootstrap argument in the above paper and the commutator estimates in [M. Visan and X. Zhang, On the blowup for the $L^2$-critical focusing nonlinear Schrödinger equation in higher dimensions below the energy class. SIAM J. Math. Anal., 39(2007), 34-56.].

Comments are welcome. arXiv admin note: text overlap with arXiv:0907.5047 by other authors

References in corpus (2)

• The mass-critical nonlinear Schrödinger equation with radial data in dimensions three and higher
• Blow-up dynamics and spectral property in the $L^2$-critical nonlinear Schrödinger equation in high dimensions