Abstract
We consider the generalized Korteweg-de Vries (gKdV) equation with the time oscillating nonlinearity:
Under the suitable assumption on g, we show that if the nonlinear term is mass critical or supercritical i.e., \({p \geq 5}\) and \({u(0) \in \dot{H}^{s_{p}}}\), where \({s_{p} = 1/2 - 2/(p-1)}\) is a scale critical exponent, then there exists a unique global solution to (gKdV) provided that \({|\omega|}\) is sufficiently large. We also obtain the behavior of the solution to (gKdV) as \({|\omega| \to \infty}\).
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J. Segata is partially supported by MEXT, Grant-in-Aid for Young Scientists (A) 25707004.
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Segata, Ji., Watanabe, K. The generalized Korteweg-de Vries equation with time oscillating nonlinearity in scale critical Sobolev space. Nonlinear Differ. Equ. Appl. 23, 51 (2016). https://doi.org/10.1007/s00030-016-0405-y
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DOI: https://doi.org/10.1007/s00030-016-0405-y