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arXiv · 0907.4098

Stable self similar blow up dynamics for slightly L^2 supercritical NLS equations

Frank Merle·Pierre Raphael·Jeremie Szeftel
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Abstract

We consider the focusing nonlinear Schrödinger equations $i\partial_t u+Δu +u|u|^{p-1}=0$ in dimension $1\leq N\leq 5$ and for slightly $L^2$ supercritical nonlinearities $p_c<p<(1+\e)p_c$ with $p_c=1+\frac{4}{N}$ and $0<\e\ll 1$. We prove the existence and stability in the energy space $H^1$ of a self similar finite time blow up dynamics and provide a qualitative description of the singularity formation near the blow up time

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Frank Merle, Pierre Raphael, Jeremie Szeftel. 2009-07-23. Stable self similar blow up dynamics for slightly L^2 supercritical NLS equations. https://arxiv.org/abs/0907.4098

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