Abstract
We consider the nonlinear biharmonic Schrödinger equation
in the critical Sobolev space \(H^s({{\mathbb {R}}}^N)\), where \(N\ge 1\), \(\mu =0\) or \(-1\), \(0<s<\min \{\frac{N}{2},8\}\) and f(u) is a nonlinear function that behaves like \(\lambda \left| u\right| ^{\alpha }u\) with \(\lambda \in {\mathbb {C}},\alpha =\frac{8}{N-2s}\). We prove the existence and uniqueness of global solutions to (BNLS) for small initial data.
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The authors sincerely thank the anonymous reviewers for their constructive revision suggestions.
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This work is partially supported by the National Natural Science Foundation of China 11771389, 11931010 and 11621101.
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Liu, X., Zhang, T. Global solutions for \(H^s\)-critical nonlinear biharmonic Schrödinger equation. Z. Angew. Math. Phys. 72, 177 (2021). https://doi.org/10.1007/s00033-021-01608-5
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DOI: https://doi.org/10.1007/s00033-021-01608-5