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arXiv · 2102.06926

On long-time behavior of solutions of the Zakharov-Rubenchik/Benney-Roskes system

María E. Martínez·José M. Palacios
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Abstract

We study decay properties for solutions to the initial value problem associated with the one-dimensional Zakharov-Rubenchik/Benney-Roskes system. We prove time-integrability in growing compact intervals of size $t^{r}$, $r<2/3$, centered on some characteristic curves coming from the underlying transport equations associated with the ZR/BR system. Additionally, we prove decay to zero of the local energy-norm in so-called far-field regions. Our results are independent of the size of the initial data and do not require any parity condition.

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María E. Martínez, José M. Palacios. 2021-02-13. On long-time behavior of solutions of the Zakharov-Rubenchik/Benney-Roskes system. https://doi.org/10.1088/1361-6544%2Fac288c

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