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- W4383164257 abstract "In this paper, we consider the Cauchy problem for the higher order nonlinear dispersive equation with the initial data in Gevrey space $ G^{sigma, s} $. First, using Tao's $ [k, Z]- $ multiplier method, we establish the basic estimate on dyadic blocks. Also, using the Fourier restriction norm method, we establish the bilinear estimate and approximate conservation law. Then, using the contraction mapping principle, iteration technique as well as the bilinear estimate, we prove the local well-posedness for the initial data $ u_0in G^{sigma, s} $ with $ sgeq -frac{11}{4}. $ Finally, based on the local well-poseness and the approximate conservation law, we obtain that the analyticity radium does not decay faster than $ t^{-frac{4}{11}} $ as time $ t $ goes to infinity. This result improves earlier ones in the literatures, such as [1], [12] and [50]." @default.
- W4383164257 created "2023-07-05" @default.
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- W4383164257 date "2023-01-01" @default.
- W4383164257 modified "2023-09-27" @default.
- W4383164257 title "Lower bounds on the radius of spatial analyticity for the higher order nonlinear dispersive equation on the real line" @default.
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- W4383164257 doi "https://doi.org/10.3934/dcdsb.2023119" @default.
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