Upper and lower $L^2$-decay bounds for a class of derivative nonlinear Schrödinger equations

Abstract

We consider the initial value problem for cubic derivative nonlinear Schrödinger equations possessing weakly dissipative structure in one space dimension. We show that the small data solution decays like $O((\log t{)}^{-1/4})$ in $L^2$ as $t\to +\infty$. Furthermore, we find that this $L^2$-decay rate is optimal by giving a lower estimate of the same order.

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Cited by in corpus (1)

• On the decay estimate for small solutions to nonlinear Klein-Gordon equations with dissipative structure