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arXiv · 0807.4916

The cubic fourth-order Schrodinger equation

Benoit Pausader
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Abstract

We investigate the cubic defocusing fourth order Schrödinger equation $iu_t + Δ^2u + |u|^2u=0$ in arbitrary space dimension $\mathbb{R}^n$ for arbitrary $H^2$ initial data. We prove that the equation is globally well-posed when $n \le 8$ and ill-posed when $n \ge 9$, with the additional important information that scattering holds true when $5 \le n \le 8$.

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Benoit Pausader. 2008-09-10. The cubic fourth-order Schrodinger equation. https://arxiv.org/abs/0807.4916

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