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arXiv · 2103.04293

Global solutions for $H^s$-critical nonlinear biharmonic Schrödinger equation

Xuan Liu·Ting Zhang
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Abstract

We consider the nonlinear biharmonic Schrödinger equation $$i\partial_tu+(Δ^2+μΔ)u+f(u)=0,\qquad (\text{BNLS})$$ in the critical Sobolev space $H^s(\R^N)$, where $N\ge1$, $μ=0$ or $-1$, $0<s<\min\{\fc N2,8\}$ and $f(u)$ is a nonlinear function that behaves like $λ\left|u\right|^αu$ with $λ\in\mathbb{C},α=\frac{8}{N-2s}$. We prove the existence and uniqueness of the global solutions to (BNLS) for the small initial data.

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Xuan Liu, Ting Zhang. 2021-03-07. Global solutions for $H^s$-critical nonlinear biharmonic Schrödinger equation. https://doi.org/10.1007/s00033-021-01608-5

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