Unconditional uniqueness of solution for $$\dot H^{s_c }$$ critical 4th order NLS in high dimensions |
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Authors: | Chao Lu Jing Lu |
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Institution: | 1. The Graduate School of China Academy of Engineering Physics, P. O. Box 2101, Beijing 100088, P. R. China;2. School of Mathematical Sciences, Beijing Normal University, Beijing 100875, P. R. China |
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Abstract: | In this paper, we study the unconditional uniqueness of solution for the Cauchy problem of Ḣsc(0 ≤ sc < 2) critical nonlinear fourth-order Schrödinger equations i∂tu + Δ2u-εu=λ|u|αu. By employing paraproduct estimates and Strichartz estimates, we prove that unconditional uniqueness of solution holds in Ct(I; Ḣsc(Rd)) for d ≥ 11 and min{1-, (8)/(d-4)} ≥ α >(-(d-4)+√4(d-4)2+64)/4. |
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Keywords: | Unconditional uniqueness paraproduct estimates Besov spaces fourth order nonlinear Schrö dinger equation |
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