María E. Martínez, José M. Palacios
Published 2021-02-13Version 1
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.
Approximate solutions to the initial value problem for some compressible flows in presence of shocks and void regions
The initial value problem for a third-order dispersive flow into compact almost Hermitian manifolds
Asymptotic study of the initial value problem to a standard one pressure model of multifluid flows in nondivergence form
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