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Unconditional uniqueness of solution for \(\dot H^{s_c }\) critical 4th order NLS in high dimensions

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Abstract

In this paper, we study the unconditional uniqueness of solution for the Cauchy problem of \(\dot H^{s_c } (0 \leqslant s_c < 2)\) critical nonlinear fourth-order Schrödinger equations i∂ t u+Δ2u−ϵu = λ|u|αu. By employing paraproduct estimates and Strichartz estimates, we prove that unconditional uniqueness of solution holds in \(C_t (I;\dot H^{s_c } (\mathbb{R}^d ))\) for d ≥ 11 and \(\min \left\{ {1^ - ,\tfrac{8} {{d - 4}}} \right\} \geqslant \alpha > \frac{{ - (d - 4) + \sqrt {(d - 4)^2 + 64} }} {4}\).

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Authors and Affiliations

  1. The Graduate School of China Academy of Engineering Physics, P. O. Box 2101, Beijing, 100088, P. R. China

    Chao Lu

  2. School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, P. R. China

    Jing Lu

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  1. Chao Lu
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  2. Jing Lu
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Correspondence to Chao Lu.

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Supported by China Postdoctoral Science Foundation (Grant No. 2017M620660)

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Lu, C., Lu, J. Unconditional uniqueness of solution for \(\dot H^{s_c }\) critical 4th order NLS in high dimensions. Acta. Math. Sin.-English Ser. 34, 1028–1036 (2018). https://doi.org/10.1007/s10114-017-7354-1

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  • DOI: https://doi.org/10.1007/s10114-017-7354-1

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