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arXiv · 0811.1849

On the decay of solutions to a class of defocusing NLS

Nicola Visciglia
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Abstract

We consider the following family of Cauchy problems: {equation*} i\partial_t u= Δu - u|u|^α, (t,x) \in \R \times \R^d {equation*} $$u(0)=φ\in H^1(\R^d)$$ where $0<α<\frac 4{d-2}$ for $d\geq 3$ and $0<α<\infty$ for $d=1,2$. We prove that the $L^r$-norms of the solutions decay as $t\to \pm \infty$, provided that $2 \frac 4d$.

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Nicola Visciglia. 2008-11-12. On the decay of solutions to a class of defocusing NLS. https://arxiv.org/abs/0811.1849

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