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arXiv · 1811.00914

Blow-up dynamics in the mass super-critical NLS equations

Kai Yang·Svetlana Roudenko·Yanxiang Zhao
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Abstract

We study stable blow-up dynamics in the $L^2$-supercritical nonlinear Schrödinger equation in various dimensions. We first investigate the profile equation and extend the result of X.-P. Wang [38] and Budd et al. [4] on the existence and local uniqueness of solutions of the cubic profile equation to other $L^2$-supercritical nonlinearities and dimensions $d \geq 2$. We then numerically observe the multi-bump structure of such solutions, and in particular, exhibit the $Q_{1,0}$ solution, a candidate for the stable blow-up profile. Next, using the dynamic rescaling method, we investigate stable blow-up solutions in the $L^2$-supercritical NLS and confirm the square root rate of the blow-up as well as the convergence of blow-up profiles to the $Q_{1,0}$ profile.

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Kai Yang, Svetlana Roudenko, Yanxiang Zhao. 2019-03-05. Blow-up dynamics in the mass super-critical NLS equations. https://doi.org/10.1016/j.physd.2019.02.015

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